if a^n+1 + b^n+1/a^n + b^n is the arithmetic mean of a and b then find n.

Answer:Arthametic mean of a,b is =(a+b)/2

from the problem

(a+b)/2=(a^n+1 +b ^n+1)/(a^n+b^n)

then (a+b)(a^n+b^n)=(a^n+1 +b ^n+1)*2

a^n(a-b)=b^n(a-b)

then (a/b)^n=1=(a/b)^0

from this equate the powers

then n=0

posted by

D.Nagesh

Find the solved examples based on arithmetic mean. ... If a1, a2, ……, an are n numbers, then the arithmetic mean (A) of these numbers is A = 1/n (a1 + a2 + a3 +… ... the common difference of this A.P., then b = a + (n + 2 – 1)d ⇒ d = b–a/n+1.