The sum of the first 20 terms of the series 1+32+74+158+3116+… is

General term of the given series 2.2r−12r,r≥0 Required sum =1+∑i=119 2.2r−12r Now ∑r=119 2.2r−12r=∑s=119 2−12r=2×19−121−12191−1/2=38+1219−1    since sum of n terms in G.P=a1-rn1-r=37+1219 Required sum=1+37+1219=38+1219