Question

Algebra 2 Infinite Sum Question....
Will write below...

Answer 1

\[\sum_{n=1}^{\infty} 3(1/2)^{n}\]

Answer 2

3/2 + 3/4 + 3/8 + 3/16 + 3/32 + 3/64 + 3/128 + 3/(2^n) + 3/(2^(n+1))....

Answer 3

sorry I forget the formal way to answer question

Answer 4

I know the answer is 3, but I don't know how to solve it algebraically, and I'm trying to explain it to someone else...

Answer 5

\[\sum_{n=1}^\infty3\left(\frac{1}{2}\right)^n=\sum_{n=0}^\infty3\left(\frac{1}{2}\right)^{n+1}=\frac{3}{2}\sum_{n=0}^\infty\left(\frac{1}{2}\right)^n=\frac{3}{2\left(1-\frac{1}{2}\right)}\]
This is using the formula for a geometric series:
\[\sum_{n=0}^\infty ar^n=\frac{a}{1-r},~\text{for }|r|<1\]