Question

The $n$-th derivative of the reciprocal of a function and a binomial identity

score 178 · Answer 1 · 2026-04-13 20:58:41

178

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The $n$-th derivative of the reciprocal of a function and a binomial identity

Published on 13 Apr 2026 - 20:58

score 725 · Answer 2 · 2026-04-12 18:34:34

725

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Pascal Triangle Vs Sierpinski Triangle

Published on 12 Apr 2026 - 18:34

score 158 · Answer 3 · 2026-04-15 22:22:32

158

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If $c$ is equal to $\binom{99}{0}-\binom{99}{2}+\binom{99}{4}-\binom{99}{6}+\cdots+\binom{99}{96}-\binom{99}{98},$ then find $\log_2{(-c)}$.

Published on 15 Apr 2026 - 22:22

score 353 · Answer 4 · 2026-04-15 12:13:45

353

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Find sum binomial coefficients

Published on 15 Apr 2026 - 12:13

score 195 · Answer 5 · 2026-04-13 06:05:38

195

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sum of binomial series of the form $\sum^{9}_{k=0}\binom{10}{10-k}(10-k)^9$

Published on 13 Apr 2026 - 6:05

score 971 · Answer 6 · 2026-04-17 02:45:56

971

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Prove that $ \sum_{k=0}^m {m \choose k} {n \choose r+k} = {m+n \choose m+r}. $

Published on 17 Apr 2026 - 2:45

score 145 · Answer 7 · 2026-04-15 01:34:58

145

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Summation of Binomial Coefficient Proof

Published on 15 Apr 2026 - 1:34

score 322 · Answer 8 · 2026-04-16 00:46:21

322

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Proving a Binomial Summation with Induction $\sum_{k=0}^n(-1)^k \binom nk^2$

Published on 16 Apr 2026 - 0:46

score 301 · Answer 9 · 2026-04-16 03:17:16

301

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Evaluate the sum $\sum_{k=1}^n {n \choose k-1} {n \choose k}$

Published on 16 Apr 2026 - 3:17

score 81 · Answer 10 · 2026-04-17 11:07:21

81

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show that $\sum_{i=1}^{n} (-1)^{i+1}{{n}\choose{i}}\frac{1}{i(i+1)} = \frac{1}{2} + \frac{1}{3} + ... + \frac{1}{n+1}$

Published on 17 Apr 2026 - 11:07

score 183 · Answer 11 · 2026-04-16 01:34:46

183

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Proving that $\sum\limits_{k=0}^{n} {{m+k} \choose{k}} = { m+n+1 \choose n }$

Published on 16 Apr 2026 - 1:34

score 300 · Answer 12 · 2026-04-12 20:37:17

300

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Simplification of binomial coefficients

Published on 12 Apr 2026 - 20:37

score 111 · Answer 13 · 2026-04-11 22:58:24

111

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Sum of Alternating Factorial Products

Published on 11 Apr 2026 - 22:58

score 1.5k · Answer 14 · 2026-04-17 05:14:30

1.5k

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Calculating the probability of drawing cards

Published on 17 Apr 2026 - 5:14

score 143 · Answer 15 · 2026-04-15 18:02:51

143

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Find equation of Pascal variation to calcuate the nth element of x row

Published on 15 Apr 2026 - 18:02

List Question

The $n$-th derivative of the reciprocal of a function and a binomial identity

Pascal Triangle Vs Sierpinski Triangle

If $c$ is equal to $\binom{99}{0}-\binom{99}{2}+\binom{99}{4}-\binom{99}{6}+\cdots+\binom{99}{96}-\binom{99}{98},$ then find $\log_2{(-c)}$.

Find sum binomial coefficients

sum of binomial series of the form $\sum^{9}_{k=0}\binom{10}{10-k}(10-k)^9$

Prove that $ \sum_{k=0}^m {m \choose k} {n \choose r+k} = {m+n \choose m+r}. $

Summation of Binomial Coefficient Proof

Proving a Binomial Summation with Induction $\sum_{k=0}^n(-1)^k \binom nk^2$

Evaluate the sum $\sum_{k=1}^n {n \choose k-1} {n \choose k}$

show that $\sum_{i=1}^{n} (-1)^{i+1}{{n}\choose{i}}\frac{1}{i(i+1)} = \frac{1}{2} + \frac{1}{3} + ... + \frac{1}{n+1}$

Proving that $\sum\limits_{k=0}^{n} {{m+k} \choose{k}} = { m+n+1 \choose n }$

Simplification of binomial coefficients

Sum of Alternating Factorial Products

Calculating the probability of drawing cards

Find equation of Pascal variation to calcuate the nth element of x row

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