Question

Can $ \lim_{n \to \infty} \sum_{i=1}^{n} (1-\frac {x_i}{\sqrt{x_i^2+r^2}}) \cdot (x_{i+1}-x_{i})$ be written as a definite integral

score 172 · Answer 1 · 2014-03-06 05:44:52

172

Views

Can $ \lim_{n \to \infty} \sum_{i=1}^{n} (1-\frac {x_i}{\sqrt{x_i^2+r^2}}) \cdot (x_{i+1}-x_{i})$ be written as a definite integral

Published on 06 Mar 2014 - 5:44

score 227 · Answer 2 · 2014-03-07 09:51:04

227

Views

How to prove $\sum\limits_{k=2}^{n}\dfrac{1}{k}<\log(n)<\sum\limits_{k=1}^{n-1}\dfrac{1}{k}$

Published on 07 Mar 2014 - 9:51

score 163 · Answer 3 · 2014-03-09 12:52:46

163

Views

$\lim\limits_{n\to\infty}\Bigl[\sin\Bigl(\dfrac{n}{n^2+1^2}\Bigr)+\sin\Bigl(\dfrac{n}{n^2+2^2}\Bigr)...+\sin\Bigl(\dfrac{n}{n^2+n^2}\Bigr)\Bigr]$

Published on 09 Mar 2014 - 12:52

score 290 · Answer 4 · 2017-04-09 20:22:00

290

Views

How can you use combinations to find a general formula for the power series summation

Published on 09 Apr 2017 - 20:22

score 6.2k · Answer 5 · 2017-04-09 20:50:40

6.2k

Views

Proof that the area under a curve is the definite integral, without the fundamental theorem of calculus

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score 173 · Answer 6 · 2017-04-10 07:52:07

173

Views

Riemann sums for sequence of functions

Published on 10 Apr 2017 - 7:52

score 211 · Answer 7 · 2017-04-13 13:38:38

211

Views

Limit of a sum 1: $\lim _{n\to \infty }\sum _{k=1}^n\sqrt{n^4+k} \cdot \sin \frac{2k\pi }{n}$

Published on 13 Apr 2017 - 13:38

score 47 · Answer 8 · 2017-04-15 12:06:59

47

Views

a question on riemann integration limits

Published on 15 Apr 2017 - 12:06

score 134 · Answer 9 · 2017-04-16 08:04:24

134

Views

Find limit of sequence using integral

Published on 16 Apr 2017 - 8:04

score 463 · Answer 10 · 2017-04-16 11:26:07

463

Views

Help proving elementray properties of the Riemann Integral using only the Riemann sums definition of the Riemann integral

Published on 16 Apr 2017 - 11:26

score 260 · Answer 11 · 2017-04-16 22:15:01

260

Views

Prove that f(x) is not continuous and differentiable at any point. Find Riemann sums.

Published on 16 Apr 2017 - 22:15

score 1k · Answer 12 · 2017-04-17 23:11:14

1k

Views

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Published on 17 Apr 2017 - 23:11

score 152 · Answer 13 · 2017-04-18 12:05:11

152

Views

Show that the function $\dfrac{1}{\sqrt{x}}$ is Riemann integrable on $[2^{-2n} , 2^{-2n+2}]$ for any positive integer $n$. #2

Published on 18 Apr 2017 - 12:05

score 127 · Answer 14 · 2017-04-21 09:58:55

127

Views

Riemann sum for integral using subintervals

Published on 21 Apr 2017 - 9:58

score 215 · Answer 15 · 2017-04-21 11:08:17

215

Views

Riemann Sum, Ergodic Theorem and Strong Law of Large Number

Published on 21 Apr 2017 - 11:08

List Question

Can $ \lim_{n \to \infty} \sum_{i=1}^{n} (1-\frac {x_i}{\sqrt{x_i^2+r^2}}) \cdot (x_{i+1}-x_{i})$ be written as a definite integral

How to prove $\sum\limits_{k=2}^{n}\dfrac{1}{k}<\log(n)<\sum\limits_{k=1}^{n-1}\dfrac{1}{k}$

$\lim\limits_{n\to\infty}\Bigl[\sin\Bigl(\dfrac{n}{n^2+1^2}\Bigr)+\sin\Bigl(\dfrac{n}{n^2+2^2}\Bigr)...+\sin\Bigl(\dfrac{n}{n^2+n^2}\Bigr)\Bigr]$

How can you use combinations to find a general formula for the power series summation

Proof that the area under a curve is the definite integral, without the fundamental theorem of calculus

Riemann sums for sequence of functions

Limit of a sum 1: $\lim _{n\to \infty }\sum _{k=1}^n\sqrt{n^4+k} \cdot \sin \frac{2k\pi }{n}$

a question on riemann integration limits

Find limit of sequence using integral

Help proving elementray properties of the Riemann Integral using only the Riemann sums definition of the Riemann integral

Prove that f(x) is not continuous and differentiable at any point. Find Riemann sums.

Riemann integral of $f(x)=2rx$

Show that the function $\dfrac{1}{\sqrt{x}}$ is Riemann integrable on $[2^{-2n} , 2^{-2n+2}]$ for any positive integer $n$. #2

Riemann sum for integral using subintervals

Riemann Sum, Ergodic Theorem and Strong Law of Large Number

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