we know that
An infinite geometric series is the sum of an infinite geometric sequence . This series would have no last term.
so
The formula for the sum of an infinite geometric series is S∞ = a1 / (1-r )
step 1
Find the common ratio r
we have
a1=8/5
a2=-4/5
a3=2/5
a4=-1/5
so
a2/a1=(-4/5)/(8/5)=-1/2
a3/a2=(2/5)/(-4/5)=-1/2
a4/a3=(-1/5)/(2/5)=-1/2
that means
r=-1/2
substitute in the formula
S∞ = a1 / (1-r )
we have
r=-1/2
a1=8/5
substitute
S∞ =(8/5) / (1+1/2)
S∞ =(8/5) / (3/2)
S∞ =16/15
the answer is 16/15