Question

Prove $\sqrt{\sum^n_{k=1}(a_k+b_k)^2} \leq \sqrt{\sum^n_{k=1}(a_k)^2} + \sqrt{\sum^n_{k=1}(b_k)^2}$.

score 232 · Answer 1 · 2026-04-09 11:23:21

232

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Prove $\sqrt{\sum^n_{k=1}(a_k+b_k)^2} \leq \sqrt{\sum^n_{k=1}(a_k)^2} + \sqrt{\sum^n_{k=1}(b_k)^2}$.

Published on 09 Apr 2026 - 11:23

score 134 · Answer 2 · 2026-04-13 21:17:10

134

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score 88 · Answer 3 · 2026-05-10 17:36:07

88

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score 63 · Answer 4 · 2026-04-10 23:56:50

63

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Which values of $\alpha$ make this integral convergent?

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score 116 · Answer 5 · 2026-04-14 17:49:53

116

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score 61 · Answer 6 · 2026-04-15 07:47:05

61

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Sum of non-integer weighted binomial coefficients

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score 100 · Answer 7 · 2026-05-04 10:00:28

100

Views

How can I express $(1+2+\dots+(k+1))^2$ using a $\sum$ instead?

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score 238 · Answer 8 · 2026-04-18 23:15:06

238

Views

How do I evaluate $\sum_{m,n\geq 1}\frac{1}{m^2n+n^2m+2mn}$

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score 299 · Answer 9 · 2026-04-17 05:28:41

299

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Evaluate the sum $\sum_{m,n\geq 1}\frac{1}{m^2n+n^2m+kmn} $

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score 169 · Answer 10 · 2026-04-14 10:49:34

169

Views

The sum of difference products related to determinants with factorials

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score 100 · Answer 11 · 2026-05-10 18:44:48

100

Views

Prove the inequality $\sum_{cyc}\frac{a^3}{b\sqrt{a^3+8}}\ge 1$

Published on 10 May 2026 - 18:44

score 42 · Answer 12 · 2026-04-12 23:31:55

42

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score 2.1k · Answer 13 · 2026-04-17 00:14:02

2.1k

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score 91 · Answer 14 · 2026-04-16 11:56:44

91

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Published on 16 Apr 2026 - 11:56

score 116 · Answer 15 · 2026-03-25 17:40:19

116

Views

Sum of the Geometrico-Factorial series

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List Question

Prove $\sqrt{\sum^n_{k=1}(a_k+b_k)^2} \leq \sqrt{\sum^n_{k=1}(a_k)^2} + \sqrt{\sum^n_{k=1}(b_k)^2}$.

Please explain how to do/calculate/read this Sigma notation?

Kronecker delta in multivariate Taylor expansion

Which values of $\alpha$ make this integral convergent?

What do the sum of the reciprocal of n squared make if n is a natural number?

Sum of non-integer weighted binomial coefficients

How can I express $(1+2+\dots+(k+1))^2$ using a $\sum$ instead?

How do I evaluate $\sum_{m,n\geq 1}\frac{1}{m^2n+n^2m+2mn}$

Evaluate the sum $\sum_{m,n\geq 1}\frac{1}{m^2n+n^2m+kmn} $

The sum of difference products related to determinants with factorials

Prove the inequality $\sum_{cyc}\frac{a^3}{b\sqrt{a^3+8}}\ge 1$

If two fourier series are equal, are the individual terms equal too?

Is there an equation for the amount of ones in a binary number?

Prove $\sum_{b=0}^{n-1}b\binom{n+1-b}{2} = \binom{n+2}{4}$

Sum of the Geometrico-Factorial series

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