Limits

Calculus Level 4

Let S n = sin ⁡ ( x ) + sin ⁡ ( 2 x ) + sin ⁡ ( 3 x ) + ⋯ + sin ⁡ ( n x ) S_n = \sin(x) + \sin(2x) + \sin (3x) + \cdots + \sin(nx) . Find the following limit:

lim ⁡ n → ∞ S 1 + S 2 + S 3 + ⋯ + S n n \large \lim_{n \to \infty} \frac{S_1 + S_2 + S_3 + \cdots + S_n}n

sin ⁡ x \sin x 1 2 tan ⁡ x 2 \frac 12 \tan \frac x2 1 2 cot ⁡ x 2 \frac 12 \cot \frac x2 e e

Subh Mandal by subh mandal , 22, India

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

2 solutions

Aryan Goyat
Jun 23, 2016

use complex and write q as [(n+1)(sin(x)+---------)-{sin(x)+2sin(2x)+--------------sin(nx)}]/n

you will get the value (sin(x)+---------)

from complex only

and of {sin(x)+2sin(2x)+--------------sin(nx)} from complex +diff

2 Helpful 1 Interesting 1 Brilliant 1 Confused

@subh mandal also provide that it is case when sin(x/2)=/0

aryan goyat - 4 years, 11 months ago
Yash Ghaghada
Sep 29, 2017

You can use the formula of sinx + sin2x + ........

i.e angles in A.P

After that it's just rearranging and simple algebra

0 Helpful 0 Interesting 1 Brilliant 1 Confused

Iaftercalculating limit won't exist e

Jaganmohan Reddy - 2 years, 4 months ago

I have done the same thing

Kumar Krish - 2 years, 1 month ago

And got the ans

Kumar Krish - 2 years, 1 month ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...