1−18+1.38.16−1.3.58.16.24+..=

Comparing the given series with 1+nx+n(n−1)1.2x2+.. We get nx=−18,n(n−1)1.2x2=1.38.16⇒nx(nx−x)=364⇒(−1/8)(−1/8−x)=3/64⇒1/8+x=3/8⇒x=3/8−1/8=2/8=1/4⇒nx=−1/8⇒n(1/4)=−1/8⇒n=−1/2 Given series =(1+x)n=(1+1/4)−1/2=(5/4)−1/2=(4/5)1/2=2/5.