List questions from telescopic-series

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If $x=1+\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+...+\frac{1}{\sqrt{1000000}}$, what is the value of $\lfloor{x}\rfloor$?

Published on 08 Dec 2019 - 20:18

150

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Solving linear recurrence relations

Published on 03 Jan 2020 - 19:53

116

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$T(n) = T(n − 4) + 1$

Published on 25 Mar 2026 - 4:25

155

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Infinity Summation problem (ANSWERED)

Published on 02 Feb 2020 - 0:40

44

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Find largest number $N$

Published on 04 Feb 2020 - 14:29

63

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Find $\left\lfloor\sum{n\over n^4+n^2+1}\right\rfloor-\left\lfloor\sum{n^2\over n^8+n^4+1}\right\rfloor$

Published on 06 Feb 2020 - 16:55

74

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Prove that $(s_2 - s_1) + (s_4 - s_3) + \cdots + (s_n - s_{n-1}) < s_n - s_1$

Published on 08 Feb 2020 - 18:36

55

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Direct proof using telescoping series for $a_n = 1 + 2^{2-n}$

Published on 22 Feb 2020 - 15:05

1.3k

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What is the complexity for the recurrence relation: T(n) = 2T(n/2) + 5n^2

Published on 24 Feb 2020 - 17:58

71

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Finding series from its sum, then finding its reciprocal's sum

Published on 25 Feb 2020 - 10:45

113

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Show that $\sum_{n=1}^\infty\frac{n}{(2n+1)!!}={1\over2}$

Published on 01 Mar 2020 - 13:10

178

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Possible telescopic sum

Published on 01 Apr 2020 - 12:30

42

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How would I prove $|a_n−a_1|+\sum_{i=1}^{n−1} |a_i−a_{i+1}|= \sum k_ia_i$?

Published on 05 Apr 2020 - 11:43

53

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Evaluate $\sum_{n = 1}^{99} \frac{2}{\sqrt{n} + \sqrt{n + 2}}.$

Published on 06 Apr 2020 - 23:05

82

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Finding a formula for $\sum_{k=1}^n(k^2-(k-1)^2)$

Published on 11 Apr 2020 - 4:27

List Question

If $x=1+\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+...+\frac{1}{\sqrt{1000000}}$, what is the value of $\lfloor{x}\rfloor$?

Solving linear recurrence relations

$T(n) = T(n − 4) + 1$

Infinity Summation problem (ANSWERED)

Find largest number $N$

Find $\left\lfloor\sum{n\over n^4+n^2+1}\right\rfloor-\left\lfloor\sum{n^2\over n^8+n^4+1}\right\rfloor$

Prove that $(s_2 - s_1) + (s_4 - s_3) + \cdots + (s_n - s_{n-1}) < s_n - s_1$

Direct proof using telescoping series for $a_n = 1 + 2^{2-n}$

What is the complexity for the recurrence relation: T(n) = 2T(n/2) + 5n^2

Finding series from its sum, then finding its reciprocal's sum

Show that $\sum_{n=1}^\infty\frac{n}{(2n+1)!!}={1\over2}$

Possible telescopic sum

How would I prove $|a_n−a_1|+\sum_{i=1}^{n−1} |a_i−a_{i+1}|= \sum k_ia_i$?

Evaluate $\sum_{n = 1}^{99} \frac{2}{\sqrt{n} + \sqrt{n + 2}}.$

Finding a formula for $\sum_{k=1}^n(k^2-(k-1)^2)$

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