help in this little problem

[Guest]

hi guys i just began to study series and i cant manage this one, i know you guys can help me
(-1)^n/(5^(2n))

[Guest]

What about that series?

[HallsofIvy]

Since you say "series", do you mean the sum [tex]\sum \frac{(-1)^n}{5^{2n}}[/tex]? If so, [tex]5^{2n}= (5^2)^n= 25^n[/tex] so the sum is [tex]\sum \left(\frac{-1}{25}\right)^n[/tex]. That is a geometric series that, with sum from n= 0 to infinity is [tex]\frac{1}{1+\frac{1}{25}}= \frac{1}{\frac{26}{25}}= \frac{26}{25}[/tex].