Most Important Selected Qs for JEE AdvancedMathematicsLimits
Let Lim _ n ( 1 2 n+1 + 1 2 n+3 + 1 2 n+5 + .+ 1 4 n-1 )= A B C , where A, B, C N . Find the least value of A+B+C .
Correct answer
5
Step-by-step solution
L= Lim _ n ( 1 2 n+1 + 1 2 n+2 + 1 2 n+3 + .+ 1 4 n )- Lim _ n ( 1 2 n+2 + 1 2 n+4 + 1 2 n+6 + . .+ 1 4 n )= Lim _ n [ 1 n _ r=1 ^ 2 n n 2 n+r - 1 n _ r=1 ^n n 2 n+2 r ]= Lim _ n [ 1 n _ r=1 ^ 2 n 1 2+ r n - 1 n _ r=1 ^n 1 2+2 ( r n ) ]= ₀^2 1 2+x d x- ₀^1 1 2+2 x d x=[ (2+x)]₀^2- 1 2 [ (1+x)]₀^1= 4- 2- 1 2 2= (2- 3 2 ) 2= 1 2 2= A B C Hence least value of A+B+C=1+2+2=5