Sequences and Series
If a, b, c are in AP, prove that a2+c2+4ac=2(ab+bc+ca).
If an=43−(43)2+(43)3+...+(−1)n−1(43)n and bn=1−an, then find the least natural number n0 such that bn>an∀n≥n0.
Assertion :STATEMENT -1 : If x,y,z are the sides of a triangle such that x+y+z=1, then [32x−1+2y−1+2z−1]≥((2x−1)(2y−1)(2z−1))1/3
Reason :STATEMENT-2 : For positive numbers their A.M., G.M. and H.M. satisfy the relation A.M.>G.M.>H.M.