Question

Evaluate the series 1+2+4+8+...+a10

Answer 1

Seems to be geometric
times 2 each time
an=a1(r)^(n-1)
a1=first term
r=common ratio
n=which one

a1=1
r=2

so

sum where
a1=first term
r=common ratio
n=which one
$S_n= \frac{a_1(1-r^n)}{1-r}$
to n=10
$S_{10}= \frac{1(1-2^10)}{1-2}$
$S_{10}= \frac{1(-1024)}{-1}$
1024 is thesum