Let the power series be given with $$\sum_{n=0}^{\infty}3^nx^n$$ Find the sum function $f(x)$.

I know that $$\sum_{n=0}^{\infty}x^n=\frac{1}{1+x}$$ but I'm not sure how to find the sum function. I hope you will help.

  • 3
    $\begingroup$ Hint: $3^n\times x^n=(3x)^n$. $\endgroup$ – lulu Jun 19 at 11:14

$$\sum_{n=0}^{\infty}3^nx^n=\sum_{n=0}^{\infty}(3x)^n=\frac{1}{1-3x}$$ provided that $|3x|<1$.

  • 1
    $\begingroup$ Consistency is important. $\endgroup$ – uniquesolution Jun 19 at 12:18

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.