Question

sum of x^n*2^n from n=1 to inf

Answer 1

remember, whenever you multiply with exponents, the exponents are added.

So, to solve your problem, you would need to take x and multiply it by 2 and then take the two "n" and add them together

2 * x is 2x
n + n = 2n

So your final answer would be 2x^2n

Answer 2

S= a/(1-r)
a is your first term so it would be a=2x
r is your common ratio (which is just the 2nd term divided by the first term) r=2x

sub it in and you would get S = 2x/(1-2x)