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

$$\mathrm{If}$$$$\mathrm{f}\left(\mathrm{x}\right)\mathrm{is}\mathrm{an}e\mathrm{ven}\mathrm{function}\mathrm{is}$$$$\underset{n=-\mathrm{\infty }}{\sum ^{\mathrm{\infty }}}f\left(n\right)=2\underset{n=0}{\sum ^{\mathrm{\infty }}}f\left(n\right)true?$$

Commented by abdomathmax last updated on 04/May/20

$$\sum _{n=-\mathrm{\infty }}^{+\mathrm{\infty }}f\left(n\right)=\sum _{n=-\mathrm{\infty }}^{0}f\left(n\right)+\sum _0^{\mathrm{\infty }}f\left(n\right)$$$$changementofindicem=-ngive$$$$\sum _{n=-\mathrm{\infty }}^0=\sum _{m=0}^{+\mathrm{\infty }}f(-m)=\sum _{m=0}^{+\mathrm{\infty }}f\left(m\right)\Rightarrow$$$$\sum _{n=-\mathrm{\infty }}^{+\mathrm{\infty }}f\left(n\right)=2\sum _{n=0}^{\mathrm{\infty }}f\left(n\right)therelstionistrue$$$$butwemusttookalooktoconvergence...$$

Commented by frc2crc last updated on 04/May/20

$$thanks$$

Commented by abdomathmax last updated on 09/May/20

$$youarewelcome$$

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