Question

cos x + cos 2x + cos 3x + ...+ cos 10x para x= π/3

Answer 1

1 + __3x - 3_ - __2x + 4__
x² + 2x + 1 x² - 1 x² + 3x + 2

___1__ + ___3(x - 1)__ - __2(x + 2)__
(x + 1)² (x + 1)(x - 1) (x + 1)(x + 2)

___1__ + ___3__ - __2__
(x + 1)² x + 1 x + 1
m.m.c ⇒ (x + 1)²

1 + 3(x + 1) - 2(x + 1)__ = __1 + 3x + 3 - 2x - 2_ = _x + 2_
(x + 1)² ( x + 1)² (x + 1)²