List questions from telescopic-series

49

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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 17 Apr 2026 - 8:40

153

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Solving linear recurrence relations

Published on 15 Apr 2026 - 7:41

126

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$T(n) = T(n − 4) + 1$

Published on 30 Apr 2026 - 6:40

159

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Infinity Summation problem (ANSWERED)

Published on 10 May 2026 - 20:57

46

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Find largest number $N$

Published on 30 Apr 2026 - 9:46

66

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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 17 Apr 2026 - 0:40

77

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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 17 Apr 2026 - 13:45

57

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

Published on 15 Apr 2026 - 12:44

1.3k

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

Published on 15 Apr 2026 - 6:57

74

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

Published on 08 Apr 2026 - 23:59

116

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

Published on 15 Apr 2026 - 8:15

180

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Possible telescopic sum

Published on 10 May 2026 - 8:35

45

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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 12 Apr 2026 - 2:40

56

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

Published on 16 Apr 2026 - 23:23

85

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

Published on 10 Apr 2026 - 16:24

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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