Calculus - Definite Integration

1357

Manish Shankar ·2014-02-13 22:14:12

Find this
1+cosx+cos2x+...+cosnx

This might help

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Soumyadeep Basu I don't understand. Please explain, Sir.
Upvote·0· Reply ·2014-02-14 02:20:21
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1357

Manish Shankar ·2014-02-14 03:07:02

sorry i meant to have find the some of the series

1+cosx+cos2x+cos3x+...+cosnx

This will provide the solution for the question

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Soumyadeep Basu Ok. Thank you Sir.
Upvote·0· Reply ·2014-02-14 05:12:08
Sourish Ghosh I think 1+cosx+cos2x+...+cosnx will only help if the either the denominator is sin(x/2) or the numerator is sin(n+1/2)2x.
Upvote·0· Reply ·2014-02-14 05:28:03
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1357

Manish Shankar ·2014-02-14 05:53:28

hmm it should have been sinx/2 only..

1133

Sourish Ghosh ·2014-02-14 05:35:24

If the sum was ₀ âˆ« ^Ï€ sin(n + 12)xsin(x2)dx
then,
1 + 2(cosx + cos2x + cos3x + ... + cosnx) = sin(n + 12)xsin(x2)

Integrate LHS to get answer as Ï€.

Definite Integration