We can split the above expression into 2 parts. We will split 2n terms into 2 parts also which will leave it as n terms and another n terms.
\(\big(\frac{3}{5} + \frac{3}{5^3} + \) ...... to n terms\(\big)\) + \(\bigg(\frac{4}{5} + \frac{4}{5^2} + .....\) to n terms\(\bigg)\)
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 = \(\frac{3}{5} , \frac{4}{5}\)
r = (ratio between the n term and n-1 term)
\(\frac{3}{5^2} \div \frac{3}{5}\), \(\frac{4}{5^2} \div \frac{4}{5} = \frac{1}{5^2}, \frac{1}{5}\) n terms