100 Suppose f(n) = log2 (3).log; (4...
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100 Suppose f(n) = log2 (3).log; (4).log, (5)....logn-1 (n) then the sum f(2k) equals k=2 (A) 5010 (B) 5050 (C) 5100 (D) 5049

JEE/Engineering Exams
Maths
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( f(n)=log _{2}(3) log _{3} 4 log _{4} 5 ldots log _{n-1} n ) ( =log _{log _{2}} frac{log 4}{log _{3}} frac{log 5}{log 4} cdots cdot log _{frac{n-1}{n-2}} frac{log _{n}}{log _{n-1}} ) ( = ) ( =frac{log n}{log 2} ) ( Rightarrow quad f(x)=frac{log n}{sqrt{alpha}} ) ( begin{aligned} sum_{k=2}^{100} fleft(2^{k}right) &=sum_{k=2}^{100} frac{log 2^{k}}{log 2}=sum_{k=2}^{100} frac{k l log 2}{log 2} &=k_{=2}^{100} k &=2+3+4+cdots+100 &=1+2+ldots+100-1 &=frac{100 times 101-1}{2} &=5049 & 0 text { phion } D end{aligned} )
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