If-f-x-is-an-even-function-is-n-f-n-2-n-0-f-n-true-

Question Number 91960 by frc2crc last updated on 04/May/20

If

f (x) is an e ven function is

\underset{n = - \infty}{\sum^{\infty}} f (n) = 2 \underset{n = 0}{\sum^{\infty}} f (n) t r u e ?

Commented by abdomathmax last updated on 04/May/20

\sum_{n = - \infty}^{+ \infty} f (n) = \sum_{n = - \infty}^{0} f (n) + \sum_{0}^{\infty} f (n)

c h a n g e m e n t o f i n d i c e m = - n g i v e

\sum_{n = - \infty}^{0} = \sum_{m = 0}^{+ \infty} f (- m) = \sum_{m = 0}^{+ \infty} f (m) \Rightarrow

\sum_{n = - \infty}^{+ \infty} f (n) = 2 \sum_{n = 0}^{\infty} f (n) t h e r e l s t i o n i s t r u e

b u t w e m u s t t o o k a l o o k t o c o n v e r g e n c e \dots

Commented by frc2crc last updated on 04/May/20

t h a n k s

Commented by abdomathmax last updated on 09/May/20

y o u a r e w e l c o m e