Let b i > 1 for i = 1, 2, ..., 101. Suppose log e b 1 , log e b 2 , ..., log e b 101 are in Arithmetic Progression (A. P.) with the common difference log e 2. Suppose a 1 , a 2 , ..., a 101 are in A.P. such that a 1 = b 1 and a 51 = b 51 . If t = b 1 + b 2 + ... + b 51 and s = a 1 + a 2 + ... + a 51 , then
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a 2 , a 3 ,....., a 50 are Arithmetic Means and b 2 , b 3 ,....., b 50 are Geometric Means between a 1 (=b 1 ) and a 51 (=b 51 )
Hence b 2 < a 2 , b 3 < a 3 .....
t<S
Also a 1 , a 51 , a 101 is an Arithmetic Progression and b 1 , b 51 , b 101 is a Geometric Progression
Since a 1 = b 1 and a 51 = b 51
b 101 >a 101
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