Question

Using Newton's binomial theorem to prove that a sum evaluates to $36^n-26^n$

score 270 · Answer 1 · 2026-03-29 04:47:21

270

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Using Newton's binomial theorem to prove that a sum evaluates to $36^n-26^n$

Published on 29 Mar 2026 - 4:47

score 689 · Answer 2 · 2014-10-01 07:41:43

689

Views

Estimating sum with binomial coefficients

Published on 01 Oct 2014 - 7:41

score 68 · Answer 3 · 2026-03-29 01:33:43

68

Views

proving counting problems?

Published on 29 Mar 2026 - 1:33

score 343 · Answer 4 · 2014-10-03 09:41:57

343

Views

Alternating sum with binomial coefficients $\sum_{k=0}^{49}(-1)^k\binom{99}{2k}$

Published on 03 Oct 2014 - 9:41

score 186 · Answer 5 · 2014-10-03 19:24:36

186

Views

difference between independent binomial variables

Published on 03 Oct 2014 - 19:24

score 366 · Answer 6 · 2014-10-03 20:42:58

366

Views

Congruence between binomial coefficient and integer part.

Published on 03 Oct 2014 - 20:42

score 267 · Answer 7 · 2026-03-29 06:55:12

267

Views

Sums with squares of binomial coefficients multiplied by a polynomial

Published on 29 Mar 2026 - 6:55

score 280 · Answer 8 · 2014-10-04 08:08:29

280

Views

Compute the double sum with binomial coefficients: $ \sum_{1\leq i,j\leq n, \ i+j\leq n }\binom{i+j}{i} x^i y^j $

Published on 04 Oct 2014 - 8:08

score 10.1k · Answer 9 · 2014-10-04 11:19:20

10.1k

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Proving $ \binom n 0 ^2 + \binom n 1 ^2 + \dots + \binom n n ^2 = \binom { 2n} n $ without induction

Published on 04 Oct 2014 - 11:19

score 5.9k · Answer 10 · 2014-10-04 13:28:20

5.9k

Views

Choice Problem: choose 5 days in a month, consecutive days are forbidden

Published on 04 Oct 2014 - 13:28

score 77 · Answer 11 · 2014-10-04 15:35:20

77

Views

Why does $ \frac{b^n-a^n}{b-a}=\sum_{k=1}^nb^{n-k}a^{k-1}$?

Published on 04 Oct 2014 - 15:35

score 815 · Answer 12 · 2014-10-04 16:45:19

815

Views

Prove that $\sum_{k=1}^nk^2{n\choose k}^2=n^2 \binom {2n-2}{n-1}$

Published on 04 Oct 2014 - 16:45

score 97 · Answer 13 · 2026-03-30 23:55:45

97

Views

Showing equivalence of two binomial expressions

Published on 30 Mar 2026 - 23:55

score 248 · Answer 14 · 2026-03-26 07:58:53

248

Views

Proof with combinatorial argument for $\binom{n}{k+1} = \binom{n-1}k+ \binom{n-2}k +...+ \binom{k}k$

Published on 26 Mar 2026 - 7:58

score 2k · Answer 15 · 2014-10-06 01:32:45

2k

Views

World series lengths competition, binomial distribution.

Published on 06 Oct 2014 - 1:32

List Question

Using Newton's binomial theorem to prove that a sum evaluates to $36^n-26^n$

Estimating sum with binomial coefficients

proving counting problems?

Alternating sum with binomial coefficients $\sum_{k=0}^{49}(-1)^k\binom{99}{2k}$

difference between independent binomial variables

Congruence between binomial coefficient and integer part.

Sums with squares of binomial coefficients multiplied by a polynomial

Compute the double sum with binomial coefficients: $ \sum_{1\leq i,j\leq n, \ i+j\leq n }\binom{i+j}{i} x^i y^j $

Proving $ \binom n 0 ^2 + \binom n 1 ^2 + \dots + \binom n n ^2 = \binom { 2n} n $ without induction

Choice Problem: choose 5 days in a month, consecutive days are forbidden

Why does $ \frac{b^n-a^n}{b-a}=\sum_{k=1}^nb^{n-k}a^{k-1}$?

Prove that $\sum_{k=1}^nk^2{n\choose k}^2=n^2 \binom {2n-2}{n-1}$

Showing equivalence of two binomial expressions

Proof with combinatorial argument for $\binom{n}{k+1} = \binom{n-1}k+ \binom{n-2}k +...+ \binom{k}k$

World series lengths competition, binomial distribution.

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