The arithmetic mean of a and b is an+bnan−1+bn−1. The value of n is
-1
0
1
a
an+bnan−1+bn−1=a+b2⇒2an+2bn=(a+b)(an−1+bn−1)⇒2an+2bn=an+ban−1+abn−1+bn⇒an+bn=anba+abnb⇒an[1−ba]=bn[ab−1]⇒an(a−ba)=bn(a−bb)⇒an−1=bn−1⇒(ab)n−1=1⇒(ab)n−1=(ab)0 ∴n−1=0∴n=1