0
$\begingroup$

Possible Duplicate:
Value of $\sum\limits_n x^n$

Ive been studying Geometric series and Arithmetic series all day and have struggled to attempt these problems. The Question is to sum up these problems.

1) \begin{align}&\sum_{n=0}^\infty 3^{-n}\end{align} 2) \begin{align}&\sum_{n=2}^\infty 3^{-n}\end{align} 3) \begin{align}&\sum_{n=0}^{n+1} 6^{n}\end{align}

Is it correct to say they are not geometric series because for 1) r=3 so r>1? So what formula do I use on these problems? I'm struggling to find the formulas to use.

Thanks. Apologies if I have asked this question the wrong way.

  • 3
    Since $3^{-n} = (\frac{1}{3})^n$, numbers 1 and 2 will converge. Number 3 is also finite, since you are summing only finitely-many terms.2012-04-06

2 Answers 2