Question

Evaluate this sum: $ \sum_{q=0}^{2n} \binom{p+l-q}{p} \binom{2n}{q}$

score 170 · Answer 1 · 2026-04-17 08:07:50

170

Views

Evaluate this sum: $ \sum_{q=0}^{2n} \binom{p+l-q}{p} \binom{2n}{q}$

Published on 17 Apr 2026 - 8:07

score 353 · Answer 2 · 2026-04-12 21:06:13

353

Views

Summation of an infinite series $\frac{x}{4^x}$

Published on 12 Apr 2026 - 21:06

score 171 · Answer 3 · 2026-04-11 03:02:19

171

Views

Generating function of squares of generalized harmonic numbers

Published on 11 Apr 2026 - 3:02

score 47 · Answer 4 · 2026-04-12 03:37:54

47

Views

Simplifying a summation

Published on 12 Apr 2026 - 3:37

score 185 · Answer 5 · 2026-04-16 23:09:35

185

Views

Calculate (express without infinite sum): $\frac{2}{1\cdot3}-\frac{4}{2 \cdot 9} + \frac{8}{3\cdot 27}- \frac{16}{4 \cdot 81} + ...$

Published on 16 Apr 2026 - 23:09

score 151 · Answer 6 · 2026-04-15 10:45:42

151

Views

How to prove $\sum_{i=1}^r (r-1)a_i^2\geq\sum_{i,j=1\\i\neq j}^r a_ja_i$?

Published on 15 Apr 2026 - 10:45

score 620 · Answer 7 · 2026-04-15 05:56:51

620

Views

How to solve the recurrence $T(n) = T(n − 2) + 1/\lg n$

Published on 15 Apr 2026 - 5:56

score 104 · Answer 8 · 2026-04-16 08:45:25

104

Views

Want help for prove formula by combinatoric argument $1\cdot 2+2\cdot 3+3\cdot 4+\dots +n(n+1)=\frac{n(n+1)(n+2)}{3}$

Published on 16 Apr 2026 - 8:45

score 1.5k · Answer 9 · 2026-04-16 14:18:01

1.5k

Views

Solving $\sum_{k=0}^n 2^k \binom{2n-k}{n}=4^n$ using generating functions

Published on 16 Apr 2026 - 14:18

score 44 · Answer 10 · 2026-04-11 16:53:55

44

Views

Positive finite sum with restriction

Published on 11 Apr 2026 - 16:53

score 248 · Answer 11 · 2026-04-14 10:33:44

248

Views

How to show $\sum_{k=1}^n \binom{n-1}{k-1} n^{n-k} k! = n^n$

Published on 14 Apr 2026 - 10:33

score 112 · Answer 12 · 2026-04-13 10:19:15

112

Views

Double Summation question from Hoffman/Kunze

Published on 13 Apr 2026 - 10:19

score 44 · Answer 13 · 2026-04-13 12:24:46

44

Views

Confusing simplification of summation

Published on 13 Apr 2026 - 12:24

score 54 · Answer 14 · 2026-04-14 09:55:01

54

Views

Show that $s_3 =\sum_{u, v, w \text{ all distinct}} a_ua_va_w \le (n-1)(n-2)\sum_{k=1}^n a_k^3 $. Generalize.

Published on 14 Apr 2026 - 9:55

score 435 · Answer 15 · 2026-04-11 19:51:11

435

Views

How does this inequality follow from Hölder's inequality?

Published on 11 Apr 2026 - 19:51

List Question

Evaluate this sum: $ \sum_{q=0}^{2n} \binom{p+l-q}{p} \binom{2n}{q}$

Summation of an infinite series $\frac{x}{4^x}$

Generating function of squares of generalized harmonic numbers

Simplifying a summation

Calculate (express without infinite sum): $\frac{2}{1\cdot3}-\frac{4}{2 \cdot 9} + \frac{8}{3\cdot 27}- \frac{16}{4 \cdot 81} + ...$

How to prove $\sum_{i=1}^r (r-1)a_i^2\geq\sum_{i,j=1\\i\neq j}^r a_ja_i$?

How to solve the recurrence $T(n) = T(n − 2) + 1/\lg n$

Want help for prove formula by combinatoric argument $1\cdot 2+2\cdot 3+3\cdot 4+\dots +n(n+1)=\frac{n(n+1)(n+2)}{3}$

Solving $\sum_{k=0}^n 2^k \binom{2n-k}{n}=4^n$ using generating functions

Positive finite sum with restriction

How to show $\sum_{k=1}^n \binom{n-1}{k-1} n^{n-k} k! = n^n$

Double Summation question from Hoffman/Kunze

Confusing simplification of summation

Show that $s_3 =\sum_{u, v, w \text{ all distinct}} a_ua_va_w \le (n-1)(n-2)\sum_{k=1}^n a_k^3 $. Generalize.

How does this inequality follow from Hölder's inequality?

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