Sum of a G.P. series is represented by the formula, Sn = a\(\frac{1-r^n}{1-r}\) , when |r|<1.
‘Sn’ represents the sum of the G.P. series up to nth terms, ‘a’ represents the first term, ‘r’ represents the common ratio and ‘n’ represents the number of terms.
Here,
a = 1
r = (ratio between the n term and n-1 term) -\(\frac{1}{2} \div 1 = -\frac{1}{2}\)
n = 9 terms