JEE Advanced 2016 Paper 2 Mathematics Q2

Mathematics

Problem

Let

b_i>1

for

i=1,2,\ldots,101

. Suppose

\log_e b_1,\log_e b_2,\ldots,\log_e b_{101}

are in Arithmetic Progression (A.P.) with the common difference

\log_e 2

. Suppose

a_1,a_2,\ldots,a_{101}

are in A.P. such that

a_1=b_1

and

a_{51}=b_{51}

. If

t=b_1+b_2+\cdots+b_{51}

and

s=a_1+a_2+\cdots+a_{51}

, then