Question

Prove that $1+\frac{1}{2^3}+\frac{1}{3^3}+\cdots+\frac{1}{2018^3}<\frac{5}{4}$

score 124 · Answer 1 · 2018-04-05 13:02:02

124

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Prove that $1+\frac{1}{2^3}+\frac{1}{3^3}+\cdots+\frac{1}{2018^3}<\frac{5}{4}$

Published on 05 Apr 2018 - 13:02

score 118 · Answer 2 · 2026-03-25 08:09:42

118

Views

Prove using mathematical induction $1\cdot2+2\cdot2^2+3\cdot2^3+\ldots+n\cdot2^n=2[1+(n-1)2^n]$

Published on 25 Mar 2026 - 8:09

score 899 · Answer 3 · 2018-04-06 01:36:30

899

Views

Total number of triangles in a triangular grid

Published on 06 Apr 2018 - 1:36

score 34 · Answer 4 · 2026-03-25 20:12:42

34

Views

Find the complex Laurent series of f(z) and show it converges to f(z)

Published on 25 Mar 2026 - 20:12

score 50 · Answer 5 · 2018-04-06 10:39:44

50

Views

Converting closed form to summation

Published on 06 Apr 2018 - 10:39

score 45 · Answer 6 · 2026-03-26 02:41:36

45

Views

Sum of rounded down numbers

Published on 26 Mar 2026 - 2:41

score 112 · Answer 7 · 2018-04-07 01:41:21

112

Views

Summation simplification in the definition of composition of linear transformation

Published on 07 Apr 2018 - 1:41

score 52 · Answer 8 · 2018-04-07 05:11:17

52

Views

Solving expression with multiple summation notations

Published on 07 Apr 2018 - 5:11

score 93 · Answer 9 · 2026-03-25 16:00:16

93

Views

An interesting extension of a combinatorics problem

Published on 25 Mar 2026 - 16:00

score 51 · Answer 10 · 2026-03-27 14:51:29

51

Views

Manipulating summations that include the magnitude squared of vectors

Published on 27 Mar 2026 - 14:51

score 164 · Answer 11 · 2018-04-07 19:04:04

164

Views

What's the mathematical formula for the sequence 3 3 6 6 12 12 24 24 etc?

Published on 07 Apr 2018 - 19:04

score 2.2k · Answer 12 · 2018-04-07 19:59:40

2.2k

Views

What's the mathematical formula for the sequence 3 6 12 18 30 42 66 90 ...?

Published on 07 Apr 2018 - 19:59

score 250 · Answer 13 · 2018-04-07 21:01:41

Find a partial sum $S_n$ that approximates the sum of the "$S$" with an error smaller than $0.1,$ and deduce if $S_n$ is smaller or greater than $S.$

score 387 · Answer 14 · 2018-04-07 22:07:20

387

Views

Sum of $\sum_{n= 1}^{\infty} \frac{(-1)^n \ln(n)}{n(n+1)}$

Published on 07 Apr 2018 - 22:07

score 58 · Answer 15 · 2026-03-26 01:03:27

58

Views

how to calculate this sum $f_{ij}=\sum\limits_{i=0}^\infty f^{(n)}_{ij}$

Published on 26 Mar 2026 - 1:03

List Question

Prove that $1+\frac{1}{2^3}+\frac{1}{3^3}+\cdots+\frac{1}{2018^3}<\frac{5}{4}$

Prove using mathematical induction $1\cdot2+2\cdot2^2+3\cdot2^3+\ldots+n\cdot2^n=2[1+(n-1)2^n]$

Total number of triangles in a triangular grid

Find the complex Laurent series of f(z) and show it converges to f(z)

Converting closed form to summation

Sum of rounded down numbers

Summation simplification in the definition of composition of linear transformation

Solving expression with multiple summation notations

An interesting extension of a combinatorics problem

Manipulating summations that include the magnitude squared of vectors

What's the mathematical formula for the sequence 3 3 6 6 12 12 24 24 etc?

What's the mathematical formula for the sequence 3 6 12 18 30 42 66 90 ...?

Find a partial sum $S_n$ that approximates the sum of the "$S$" with an error smaller than $0.1,$ and deduce if $S_n$ is smaller or greater than $S.$

Sum of $\sum_{n= 1}^{\infty} \frac{(-1)^n \ln(n)}{n(n+1)}$

how to calculate this sum $f_{ij}=\sum\limits_{i=0}^\infty f^{(n)}_{ij}$

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