How do I find the sum of the series: (sum. n=1, infinity) [2^(n+1)]/pi^n
This looks to be a geometric series, and you are trying to find the sum as it goes to infinite. So lets break it down
Now If you can remember properties of exponents we can transform the numerator to help us
We can pull that out as a constant multiplicative of this geometric series
We can use another property of exponents here
Now the rest is easy, Our constant multiple lets call it a which is the first term in the series, is
and your common ration r is , now if we recall the formula for a sum of the geometric series as it goes to infinity
You should be able to get the rest