Question

How to prove the inequality $2\sqrt{n + 1} − 2 \le 1 +\frac 1 {\sqrt 2}+\frac 1 {\sqrt 3}+ \dots +\frac 1 {\sqrt n} \le 2\sqrt n − 1$?

score 2.7k · Answer 1 · 2026-04-17 01:00:18

2.7k

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How to prove the inequality $2\sqrt{n + 1} − 2 \le 1 +\frac 1 {\sqrt 2}+\frac 1 {\sqrt 3}+ \dots +\frac 1 {\sqrt n} \le 2\sqrt n − 1$?

Published on 17 Apr 2026 - 1:00

score 185 · Answer 2 · 2026-04-10 23:30:48

185

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Closed form of a sum

Published on 10 Apr 2026 - 23:30

score 73 · Answer 3 · 2026-04-10 16:53:25

73

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Converting Summation to Expression

Published on 10 Apr 2026 - 16:53

score 1.6k · Answer 4 · 2026-04-10 04:28:08

1.6k

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Is there a Sum Factorial?

Published on 10 Apr 2026 - 4:28

score 7.5k · Answer 5 · 2026-04-15 08:25:57

7.5k

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Induction proof for a summation: $\sum_{i=1}^n i^3 = \left[\sum_{i=1}^n i\right]^2$

Published on 15 Apr 2026 - 8:25

score 1.9k · Answer 6 · 2026-04-15 04:03:31

1.9k

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Plotting discrete time signals involving sumations in matlab.

Published on 15 Apr 2026 - 4:03

score 79 · Answer 7 · 2026-04-09 22:05:24

79

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Control ratio of geometric series through its sum

Published on 09 Apr 2026 - 22:05

score 845 · Answer 8 · 2026-04-15 12:55:30

845

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How to prove $\sum_{k=1}^{N} \frac{\sin n\theta}{2^N}=\frac{2^{N+1}\sin \theta + \sin N\theta -2\sin(N+1)\theta}{2^N(5-4\cos \theta)}$

Published on 15 Apr 2026 - 12:55

score 457 · Answer 9 · 2026-04-16 17:54:20

457

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Integration of $x^a$ and Summation of first $n$ $a$th powers

Published on 16 Apr 2026 - 17:54

score 180 · Answer 10 · 2026-04-13 07:14:16

180

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find the sum of series

Published on 13 Apr 2026 - 7:14

score 43 · Answer 11 · 2026-04-11 23:05:45

43

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Equivalence of summations

Published on 11 Apr 2026 - 23:05

score 102 · Answer 12 · 2026-04-17 02:55:59

102

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Find $S=\frac{1}{2}+\frac{3}{2^2}+\frac{5}{2^3}+\frac{7}{2^4}+...+\frac{2n-1}{2^n}+...$

Published on 17 Apr 2026 - 2:55

score 31.5k · Answer 13 · 2026-04-11 21:45:48

31.5k

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Finding the infinite sum of $e^{-n}$ using integrals

Published on 11 Apr 2026 - 21:45

score 1.2k · Answer 14 · 2026-04-14 22:46:01

1.2k

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Intersection of two lines and the minimum of the sum of the two.

Published on 14 Apr 2026 - 22:46

score 46 · Answer 15 · 2026-04-13 00:13:36

46

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sum of two equal digit numbers vs. sum of those digits

Published on 13 Apr 2026 - 0:13

List Question

How to prove the inequality $2\sqrt{n + 1} − 2 \le 1 +\frac 1 {\sqrt 2}+\frac 1 {\sqrt 3}+ \dots +\frac 1 {\sqrt n} \le 2\sqrt n − 1$?

Closed form of a sum

Converting Summation to Expression

Is there a Sum Factorial?

Induction proof for a summation: $\sum_{i=1}^n i^3 = \left[\sum_{i=1}^n i\right]^2$

Plotting discrete time signals involving sumations in matlab.

Control ratio of geometric series through its sum

How to prove $\sum_{k=1}^{N} \frac{\sin n\theta}{2^N}=\frac{2^{N+1}\sin \theta + \sin N\theta -2\sin(N+1)\theta}{2^N(5-4\cos \theta)}$

Integration of $x^a$ and Summation of first $n$ $a$th powers

find the sum of series

Equivalence of summations

Find $S=\frac{1}{2}+\frac{3}{2^2}+\frac{5}{2^3}+\frac{7}{2^4}+...+\frac{2n-1}{2^n}+...$

Finding the infinite sum of $e^{-n}$ using integrals

Intersection of two lines and the minimum of the sum of the two.

sum of two equal digit numbers vs. sum of those digits

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