Most Important Selected Qs for JEE AdvancedMathematicsSequences and Series
Let S denote sum of the series 3 2^3 + 4 2^4 3 + 5 2^6 3 + 6 2^7 5 + Compute the value of S ⁻¹ .
Correct answer
02
Step-by-step solution
Let S = _ r =1 ^ r +2 2^ r +1 r ( r +1) = _ r =1 ^ 2( r +1)- r 2^ r +1 r ( r +1) = _ r =1 ^ 1 2^ r +1 ( 2 r - 1 r +1 )= _ r =1 ^ ( 1 2^ r r - 1 2^ r +1 ( r +1) )= Lim _ n [ ( 1 2^1 1 - 1 2^2 2 )+ ( 1 2^2 2 - 1 2^3 3 ) ]+ ( 1 2^3 3 - 1 2^4 4 )+ .+ ( 1 2^n n - 1 2^ n+1 (n+1) )= Lim _ n ( 1 2 - 1 2^ n+1 9 n+1 ) S = 1 2 Hence ⁻¹=2