Question

How do I find the sum of this series?Question D

Answer 1

Sum of an infinite geometric sequence with the common ratio r, and the first term a1 is $\frac{a_1}{1-r}$

we notice
-2 times -1/4=1/2,
1/2 times -1/4=-1/8
so a1=-2
r=-1/4 or -0.25

so the sum is
$\frac{-2}{1-(-0.25)}$=
$\frac{-2}{1+0.25}$=
$\frac{-2}{1.25}$=
$\frac{-8}{5}$=
the sum is -8/5 or -1.6