{{c1::\(\sum_{i = 1}^{n} 1\)}} \(=\) \(n\)
Note 1: ETH::A&D
Deck: ETH::A&D
Note Type: Horvath Cloze
GUID:
modified
Note Type: Horvath Cloze
GUID:
c&0A&-=*J^
Before
Front
Back
{{c1::\(\sum_{i = 1}^{n} 1\)}} \(=\) \(n\)
After
Front
{{c1::\(\sum_{i = 1}^{n} 1\)}} \(=\) \(n\) (Sum)
Back
{{c1::\(\sum_{i = 1}^{n} 1\)}} \(=\) \(n\) (Sum)
Field-by-field Comparison
| Field | Before | After |
|---|---|---|
| Text | {{c1::\(\sum_{i = 1}^{n} 1\)}} \(=\) {{c2:: \(n\)}} | {{c1::\(\sum_{i = 1}^{n} 1\)}} \(=\) {{c2:: \(n\)}} (Sum) |
Note 2: ETH::A&D
Deck: ETH::A&D
Note Type: Horvath Cloze
GUID:
modified
Note Type: Horvath Cloze
GUID:
i3K1KB$5&t
Before
Front
{{c1::\(\sum_{i = 1}^{n} \sum_{i = 1}^{n} 1\)}} \(=\) \(n^2\)
Back
{{c1::\(\sum_{i = 1}^{n} \sum_{i = 1}^{n} 1\)}} \(=\) \(n^2\)
After
Front
{{c1::\(\sum_{i = 1}^{n} \sum_{i = 1}^{n} 1\)}} \(=\) \(n^2\) (Sum)
Back
{{c1::\(\sum_{i = 1}^{n} \sum_{i = 1}^{n} 1\)}} \(=\) \(n^2\) (Sum)
Field-by-field Comparison
| Field | Before | After |
|---|---|---|
| Text | {{c1::\(\sum_{i = 1}^{n} \sum_{i = 1}^{n} 1\)}} \(=\) {{c2:: \(n^2\)}} | {{c1::\(\sum_{i = 1}^{n} \sum_{i = 1}^{n} 1\)}} \(=\) {{c2:: \(n^2\)}} (Sum) |
Note 3: ETH::A&D
Deck: ETH::A&D
Note Type: Horvath Cloze
GUID:
modified
Note Type: Horvath Cloze
GUID:
CaRvZ82Z-e
Before
Front
{{c1:: \(\sum_{i = 1}^{n} \sum_{i = 1}^{n} \sum_{i = 1}^{n} 1\)}} \(=\) \(n^3\)
Back
{{c1:: \(\sum_{i = 1}^{n} \sum_{i = 1}^{n} \sum_{i = 1}^{n} 1\)}} \(=\) \(n^3\)
After
Front
{{c1:: \(\sum_{i = 1}^{n} \sum_{i = 1}^{n} \sum_{i = 1}^{n} 1\)}} \(=\) \(n^3\) (Sum)
Back
{{c1:: \(\sum_{i = 1}^{n} \sum_{i = 1}^{n} \sum_{i = 1}^{n} 1\)}} \(=\) \(n^3\) (Sum)
Field-by-field Comparison
| Field | Before | After |
|---|---|---|
| Text | {{c1:: \(\sum_{i = 1}^{n} \sum_{i = 1}^{n} \sum_{i = 1}^{n} 1\)}} \(=\) {{c2:: \(n^3\)}} | {{c1:: \(\sum_{i = 1}^{n} \sum_{i = 1}^{n} \sum_{i = 1}^{n} 1\)}} \(=\) {{c2:: \(n^3\)}} (Sum) |
Note 4: ETH::A&D
Deck: ETH::A&D
Note Type: Horvath Cloze
GUID:
modified
Note Type: Horvath Cloze
GUID:
u2lDE>&5/e
Before
Front
{{c1:: \(\sum_{j = 1}^{n} \sum_{k = \textbf{j} }^{n} 1\)}} \(=\) {{c2:: \(\sum_{j = 1}^n (n - j + 1) = \frac{n(n + 1)}{2}\)}}
Back
{{c1:: \(\sum_{j = 1}^{n} \sum_{k = \textbf{j} }^{n} 1\)}} \(=\) {{c2:: \(\sum_{j = 1}^n (n - j + 1) = \frac{n(n + 1)}{2}\)}}
inner loop depends on outer
After
Front
{{c1:: \(\sum_{j = 1}^{n} \sum_{k = \textbf{j} }^{n} 1\)}} \(=\) {{c2:: \(\sum_{j = 1}^n (n - j + 1) = \frac{n(n + 1)}{2}\)}} (Sum)
Back
{{c1:: \(\sum_{j = 1}^{n} \sum_{k = \textbf{j} }^{n} 1\)}} \(=\) {{c2:: \(\sum_{j = 1}^n (n - j + 1) = \frac{n(n + 1)}{2}\)}} (Sum)
inner loop depends on outer
Field-by-field Comparison
| Field | Before | After |
|---|---|---|
| Text | {{c1:: \(\sum_{j = 1}^{n} \sum_{k = \textbf{j} }^{n} 1\)}} \(=\) {{c2:: \(\sum_{j = 1}^n (n - j + 1) = \frac{n(n + 1)}{2}\)}} | {{c1:: \(\sum_{j = 1}^{n} \sum_{k = \textbf{j} }^{n} 1\)}} \(=\) {{c2:: \(\sum_{j = 1}^n (n - j + 1) = \frac{n(n + 1)}{2}\)}} (Sum) |
Note 5: ETH::A&D
Deck: ETH::A&D
Note Type: Horvath Cloze
GUID:
modified
Note Type: Horvath Cloze
GUID:
NU;6ob<^n3
Before
Front
{{c1:: \(\sum_{i = 1}^{n} \sum_{k = 1}^{\textbf{i} } 1\)}} \(=\) {{c2:: \(\sum_{i = 1}^n i = \frac{n(n + 1)}{2}\)}}
Back
{{c1:: \(\sum_{i = 1}^{n} \sum_{k = 1}^{\textbf{i} } 1\)}} \(=\) {{c2:: \(\sum_{i = 1}^n i = \frac{n(n + 1)}{2}\)}}
inner loop depends on outer
After
Front
{{c1:: \(\sum_{i = 1}^{n} \sum_{k = 1}^{\textbf{i} } 1\)}} \(=\) {{c2:: \(\sum_{i = 1}^n i = \frac{n(n + 1)}{2}\)}} (Sum)
Back
{{c1:: \(\sum_{i = 1}^{n} \sum_{k = 1}^{\textbf{i} } 1\)}} \(=\) {{c2:: \(\sum_{i = 1}^n i = \frac{n(n + 1)}{2}\)}} (Sum)
inner loop depends on outer
Field-by-field Comparison
| Field | Before | After |
|---|---|---|
| Text | {{c1:: \(\sum_{i = 1}^{n} \sum_{k = 1}^{\textbf{i} } 1\)}} \(=\) {{c2:: \(\sum_{i = 1}^n i = \frac{n(n + 1)}{2}\)}} | {{c1:: \(\sum_{i = 1}^{n} \sum_{k = 1}^{\textbf{i} } 1\)}} \(=\) {{c2:: \(\sum_{i = 1}^n i = \frac{n(n + 1)}{2}\)}} (Sum) |
Note 6: ETH::A&D
Deck: ETH::A&D
Note Type: Horvath Cloze
GUID:
modified
Note Type: Horvath Cloze
GUID:
n!`Y!GEmVs
Before
Front
{{c1:: \(\sum_{i = 1}^{n} i\)}} \(=\) {{c2::\(\frac{n(n + 1)}{2}\)}}
Back
{{c1:: \(\sum_{i = 1}^{n} i\)}} \(=\) {{c2::\(\frac{n(n + 1)}{2}\)}}
After
Front
{{c1:: \(\sum_{i = 1}^{n} i\)}} \(=\) {{c2::\(\frac{n(n + 1)}{2}\)}} (Sum)
Back
{{c1:: \(\sum_{i = 1}^{n} i\)}} \(=\) {{c2::\(\frac{n(n + 1)}{2}\)}} (Sum)
Field-by-field Comparison
| Field | Before | After |
|---|---|---|
| Text | {{c1:: \(\sum_{i = 1}^{n} i\)}} \(=\) {{c2::\(\frac{n(n + 1)}{2}\)}} | {{c1:: \(\sum_{i = 1}^{n} i\)}} \(=\) {{c2::\(\frac{n(n + 1)}{2}\)}} (Sum) |
Note 7: ETH::A&D
Deck: ETH::A&D
Note Type: Horvath Cloze
GUID:
modified
Note Type: Horvath Cloze
GUID:
B9BorfLC*u
Before
Front
{{c1:: \(\sum_{i = 1}^{n} i\)}} \(\leq\) \(O(n^2)\)
Back
{{c1:: \(\sum_{i = 1}^{n} i\)}} \(\leq\) \(O(n^2)\)
After
Front
{{c1:: \(\sum_{i = 1}^{n} i\)}} \(\leq\) \(O(n^2)\) (Sum)
Back
{{c1:: \(\sum_{i = 1}^{n} i\)}} \(\leq\) \(O(n^2)\) (Sum)
Field-by-field Comparison
| Field | Before | After |
|---|---|---|
| Text | {{c1:: \(\sum_{i = 1}^{n} i\)}} \(\leq\) {{c2::\(O(n^2)\)}} | {{c1:: \(\sum_{i = 1}^{n} i\)}} \(\leq\) {{c2::\(O(n^2)\)}} (Sum) |
Note 8: ETH::A&D
Deck: ETH::A&D
Note Type: Horvath Cloze
GUID:
modified
Note Type: Horvath Cloze
GUID:
Jm.C(wC@Lp
Before
Front
{{c1:: \(\sum_{i = 1}^{n} i^2\)}} \(=\) {{c2::\(\frac{n(n + 1)(2n + 1)}{6}\)}}
Back
{{c1:: \(\sum_{i = 1}^{n} i^2\)}} \(=\) {{c2::\(\frac{n(n + 1)(2n + 1)}{6}\)}}
After
Front
{{c1:: \(\sum_{i = 1}^{n} i^2\)}} \(=\) {{c2::\(\frac{n(n + 1)(2n + 1)}{6}\)}} (Sum)
Back
{{c1:: \(\sum_{i = 1}^{n} i^2\)}} \(=\) {{c2::\(\frac{n(n + 1)(2n + 1)}{6}\)}} (Sum)
Field-by-field Comparison
| Field | Before | After |
|---|---|---|
| Text | {{c1:: \(\sum_{i = 1}^{n} i^2\)}} \(=\) {{c2::\(\frac{n(n + 1)(2n + 1)}{6}\)}} | {{c1:: \(\sum_{i = 1}^{n} i^2\)}} \(=\) {{c2::\(\frac{n(n + 1)(2n + 1)}{6}\)}} (Sum) |
Note 9: ETH::A&D
Deck: ETH::A&D
Note Type: Horvath Cloze
GUID:
modified
Note Type: Horvath Cloze
GUID:
cF,b)K]Ha!
Before
Front
{{c1:: \(\sum_{i = 1}^{n} i^2\)}} \(\leq\) \(O(n^3)\)
Back
{{c1:: \(\sum_{i = 1}^{n} i^2\)}} \(\leq\) \(O(n^3)\)
After
Front
{{c1:: \(\sum_{i = 1}^{n} i^2\)}} \(\leq\) \(O(n^3)\) (Sum)
Back
{{c1:: \(\sum_{i = 1}^{n} i^2\)}} \(\leq\) \(O(n^3)\) (Sum)
Field-by-field Comparison
| Field | Before | After |
|---|---|---|
| Text | {{c1:: \(\sum_{i = 1}^{n} i^2\)}} \(\leq\) {{c2::\(O(n^3)\)}} | {{c1:: \(\sum_{i = 1}^{n} i^2\)}} \(\leq\) {{c2::\(O(n^3)\)}} (Sum) |
Note 10: ETH::A&D
Deck: ETH::A&D
Note Type: Horvath Cloze
GUID:
modified
Note Type: Horvath Cloze
GUID:
E>+A_WABT2
Before
Front
{{c1:: \(\sum_{i = 1}^{n} i^3\)}} \(=\) {{c2::\(\frac{n^2(n + 1)^2}{4}\)}}
Back
{{c1:: \(\sum_{i = 1}^{n} i^3\)}} \(=\) {{c2::\(\frac{n^2(n + 1)^2}{4}\)}}
After
Front
{{c1:: \(\sum_{i = 1}^{n} i^3\)}} \(=\) {{c2::\(\frac{n^2(n + 1)^2}{4}\)}} (Sum)
Back
{{c1:: \(\sum_{i = 1}^{n} i^3\)}} \(=\) {{c2::\(\frac{n^2(n + 1)^2}{4}\)}} (Sum)
Field-by-field Comparison
| Field | Before | After |
|---|---|---|
| Text | {{c1:: \(\sum_{i = 1}^{n} i^3\)}} \(=\) {{c2::\(\frac{n^2(n + 1)^2}{4}\)}} | {{c1:: \(\sum_{i = 1}^{n} i^3\)}} \(=\) {{c2::\(\frac{n^2(n + 1)^2}{4}\)}} (Sum) |
Note 11: ETH::A&D
Deck: ETH::A&D
Note Type: Horvath Cloze
GUID:
modified
Note Type: Horvath Cloze
GUID:
C}:U@+B*;Q
Before
Front
{{c1:: \(\sum_{i = 1}^{n} i^3\)}} \(\leq\) \(O(n^4)\)
Back
{{c1:: \(\sum_{i = 1}^{n} i^3\)}} \(\leq\) \(O(n^4)\)
After
Front
{{c1:: \(\sum_{i = 1}^{n} i^3\)}} \(\leq\) \(O(n^4)\) (Sum)
Back
{{c1:: \(\sum_{i = 1}^{n} i^3\)}} \(\leq\) \(O(n^4)\) (Sum)
Field-by-field Comparison
| Field | Before | After |
|---|---|---|
| Text | {{c1:: \(\sum_{i = 1}^{n} i^3\)}} \(\leq\) {{c2::\(O(n^4)\)}} | {{c1:: \(\sum_{i = 1}^{n} i^3\)}} \(\leq\) {{c2::\(O(n^4)\)}} (Sum) |
Note 12: ETH::A&D
Deck: ETH::A&D
Note Type: Horvath Cloze
GUID:
modified
Note Type: Horvath Cloze
GUID:
Jp{gN:I7yh
Before
Front
{{c1:: \(\sum_{i = 1}^{n} \log(i)\)}} \(=\) \(\log(n!)\)
Back
{{c1:: \(\sum_{i = 1}^{n} \log(i)\)}} \(=\) \(\log(n!)\)
After
Front
{{c1:: \(\sum_{i = 1}^{n} \log(i)\)}} \(=\) \(\log(n!)\) (Sum)
Back
{{c1:: \(\sum_{i = 1}^{n} \log(i)\)}} \(=\) \(\log(n!)\) (Sum)
Field-by-field Comparison
| Field | Before | After |
|---|---|---|
| Text | {{c1:: \(\sum_{i = 1}^{n} \log(i)\)}} \(=\) {{c2::\(\log(n!)\)}} | {{c1:: \(\sum_{i = 1}^{n} \log(i)\)}} \(=\) {{c2::\(\log(n!)\)}} (Sum) |
Note 13: ETH::A&D
Deck: ETH::A&D
Note Type: Horvath Cloze
GUID:
modified
Note Type: Horvath Cloze
GUID:
yg-tkTB|,7
Before
Front
{{c1:: \(\sum_{i = 1}^{n} i\log(i)\)}} \(\leq\) {{c2::\(\sum_{i = 1}^n n \log(n) = n^2 \log n\)}}
Back
{{c1:: \(\sum_{i = 1}^{n} i\log(i)\)}} \(\leq\) {{c2::\(\sum_{i = 1}^n n \log(n) = n^2 \log n\)}}
After
Front
{{c1:: \(\sum_{i = 1}^{n} i\log(i)\)}} \(\leq\) {{c2::\(\sum_{i = 1}^n n \log(n) = n^2 \log n\)}} (Sum)
Back
{{c1:: \(\sum_{i = 1}^{n} i\log(i)\)}} \(\leq\) {{c2::\(\sum_{i = 1}^n n \log(n) = n^2 \log n\)}} (Sum)
Field-by-field Comparison
| Field | Before | After |
|---|---|---|
| Text | {{c1:: \(\sum_{i = 1}^{n} i\log(i)\)}} \(\leq\) {{c2::\(\sum_{i = 1}^n n \log(n) = n^2 \log n\)}} | {{c1:: \(\sum_{i = 1}^{n} i\log(i)\)}} \(\leq\) {{c2::\(\sum_{i = 1}^n n \log(n) = n^2 \log n\)}} (Sum) |
Note 14: ETH::A&D
Deck: ETH::A&D
Note Type: Horvath Cloze
GUID:
modified
Note Type: Horvath Cloze
GUID:
M,?u9cw(S%
Before
Front
{{c1:: \(\sum_{i = 1}^{n} i\log(i)\)}} \(\leq\) \(O(n \log(n))\)
Back
{{c1:: \(\sum_{i = 1}^{n} i\log(i)\)}} \(\leq\) \(O(n \log(n))\)
After
Front
{{c1:: \(\sum_{i = 1}^{n} i\log(i)\)}} \(\leq\) \(O(n \log(n))\) (Sum)
Back
{{c1:: \(\sum_{i = 1}^{n} i\log(i)\)}} \(\leq\) \(O(n \log(n))\) (Sum)
Field-by-field Comparison
| Field | Before | After |
|---|---|---|
| Text | {{c1:: \(\sum_{i = 1}^{n} i\log(i)\)}} \(\leq\) {{c2::\(O(n \log(n))\)}} | {{c1:: \(\sum_{i = 1}^{n} i\log(i)\)}} \(\leq\) {{c2::\(O(n \log(n))\)}} (Sum) |