Question

Partition power series $\sum \beta^i=\frac1{1-\beta}$ into three subseries, each with sum $\frac13\frac1{1-\beta}$

score 58 · Answer 1 · 2016-11-30 18:29:30

58

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Partition power series $\sum \beta^i=\frac1{1-\beta}$ into three subseries, each with sum $\frac13\frac1{1-\beta}$

Published on 30 Nov 2016 - 18:29

score 47 · Answer 2 · 2016-12-04 14:48:16

47

Views

Given $p>1$, why is $\sum\limits_{k=1}^{p}\frac{1}{(n+1)^{k}}< \frac{1}{n}$

Published on 04 Dec 2016 - 14:48

score 2.6k · Answer 3 · 2016-12-06 06:46:38

2.6k

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If ${1+x^2=\sqrt3x}$, then $\sum_{n=1}^{24}(x^n-\frac{1}{x^n})$

Published on 06 Dec 2016 - 6:46

score 13.5k · Answer 4 · 2016-12-07 07:01:07

13.5k

Views

Representing the areas of Sierpinski triangles as a partial sum of a geometric sequence?

Published on 07 Dec 2016 - 7:01

score 75 · Answer 5 · 2026-03-26 01:23:21

75

Views

Prove that $ (\frac{1+\sqrt5}{2})^{n}+(\frac{1+\sqrt5}{2})^{n-1} = (\frac{1+\sqrt5}{2})^{n+1}$.

Published on 26 Mar 2026 - 1:23

score 275 · Answer 6 · 2016-12-15 22:41:25

275

Views

Mathematical Induction with Exponents: $1 + \frac12 + \frac14 + \dots + \frac1{2^{n}} = 2 - \frac1{2^{n}}$

Published on 15 Dec 2016 - 22:41

score 67 · Answer 7 · 2016-12-19 01:37:36

67

Views

Infinitely Many Terms in Two Sequences Which Differ by Two

Published on 19 Dec 2016 - 1:37

score 402 · Answer 8 · 2016-12-19 16:17:45

402

Views

Hall and Knight- Higher Algebra Problem 23, Example V. b

Published on 19 Dec 2016 - 16:17

score 1.4k · Answer 9 · 2016-12-20 18:06:41

1.4k

Views

Where do the arithmetic and geometric series formulas come from? Was their discovery by chance?

Published on 20 Dec 2016 - 18:06

score 112 · Answer 10 · 2017-01-03 14:56:24

112

Views

Evaluating $\lim\limits_{n\to \infty }\sum\limits_{k=0}^n\:(2n)^{-k}\binom{n}{k}$

Published on 03 Jan 2017 - 14:56

score 76 · Answer 11 · 2017-01-05 21:26:17

76

Views

Does proving that a triangle is in AP or GP have any significant meaning?

Published on 05 Jan 2017 - 21:26

score 205 · Answer 12 · 2017-01-13 01:54:22

205

Views

Geometric Progression prove the answer

Published on 13 Jan 2017 - 1:54

score 56 · Answer 13 · 2017-01-16 19:40:31

56

Views

Continuity points of function 5

Published on 16 Jan 2017 - 19:40

score 38 · Answer 14 · 2017-01-19 22:02:13

38

Views

Calculating annuity payments with payment inflation and final value of zero

Published on 19 Jan 2017 - 22:02

score 336 · Answer 15 · 2017-02-01 21:41:24

336

Views

Find the sum of the geometric sequence

Published on 01 Feb 2017 - 21:41

List Question

Partition power series $\sum \beta^i=\frac1{1-\beta}$ into three subseries, each with sum $\frac13\frac1{1-\beta}$

Given $p>1$, why is $\sum\limits_{k=1}^{p}\frac{1}{(n+1)^{k}}< \frac{1}{n}$

If ${1+x^2=\sqrt3x}$, then $\sum_{n=1}^{24}(x^n-\frac{1}{x^n})$

Representing the areas of Sierpinski triangles as a partial sum of a geometric sequence?

Prove that $ (\frac{1+\sqrt5}{2})^{n}+(\frac{1+\sqrt5}{2})^{n-1} = (\frac{1+\sqrt5}{2})^{n+1}$.

Mathematical Induction with Exponents: $1 + \frac12 + \frac14 + \dots + \frac1{2^{n}} = 2 - \frac1{2^{n}}$

Infinitely Many Terms in Two Sequences Which Differ by Two

Hall and Knight- Higher Algebra Problem 23, Example V. b

Where do the arithmetic and geometric series formulas come from? Was their discovery by chance?

Evaluating $\lim\limits_{n\to \infty }\sum\limits_{k=0}^n\:(2n)^{-k}\binom{n}{k}$

Does proving that a triangle is in AP or GP have any significant meaning?

Geometric Progression prove the answer

Continuity points of function 5

Calculating annuity payments with payment inflation and final value of zero

Find the sum of the geometric sequence

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