0If GM, AM and HM are the Geometric Mean, Arithmetic Mean and Harmonic Mean of two positive numbers respectively, then,
GM2 = AM × HM
Three numbers a, b and c are in AP if b=a+c2">b=a+c/2
Three non-zero numbers a, b and c are in HP if b=2aca+c">b=2ac/a+c
Three non-zero numbers a, b and c are in HP if a−bb−c=ac">a−b/b−c=ac
a−bb−c=ac">Let A, G and H be the AM, GM and HM between two distinct positive numbers. Then
(1) A > G > H
(2) A, G and H are in GP
a−bb−c=ac">If a series is both an AP and GP, all terms of the series will be equal. In other words, it will be a constant sequence.
a−bb−c=ac">Power Series : Important formulas
1+1+1+â?¯ n terms">1+1+1+â?¯ n terms
a−bb−c=ac">=∑1=n">=∑1=n
a−bb−c=ac">
1+2+3+â?¯+n">1+2+3+â?¯+n
a−bb−c=ac">=∑n=n(n+1)2">=∑n=n(n+1)2
a−bb−c=ac">
12+22+32+â?¯+n2">12+22+32+â?¯+n2
a−bb−c=ac">=∑n2=n(n+1)(2n+1)6">=∑n2=n(n+1)(2n+1)6
