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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 even function is  Σ_(n=−∞) ^∞ f(n)=2Σ_(n=0) ^∞ f(n) true?
Iff(x)isanevenfunctionisn=f(n)=2n=0f(n)true?
Commented by abdomathmax last updated on 04/May/20
Σ_(n=−∞) ^(+∞)  f(n) =Σ_(n=−∞) ^0  f(n) +Σ_0 ^∞  f(n)  changement of  indice m=−n give  Σ_(n=−∞) ^0  =Σ_(m=0) ^(+∞)  f(−m) =Σ_(m=0) ^(+∞ ) f(m) ⇒  Σ_(n=−∞) ^(+∞)  f(n) =2Σ_(n=0) ^∞  f(n) the relstion is true  but  we must took a look to convergence...
n=+f(n)=n=0f(n)+0f(n)changementofindicem=ngiven=0=m=0+f(m)=m=0+f(m)n=+f(n)=2n=0f(n)therelstionistruebutwemusttookalooktoconvergence
Commented by frc2crc last updated on 04/May/20
thanks
thanks
Commented by abdomathmax last updated on 09/May/20
you are welcome
youarewelcome

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