Manipal MET2017MathematicsLimits

_ n [ 1 n+1 + 1 n+2 + + 1 6 n ]

Options

A2
B(1+ 5 )
C6
D0

Correct answer

C. 6

Step-by-step solution

aligned & _ n [ 1 n+1 + 1 n+2 + + 1 n+5 n ] = & _ n _ r=0 ^ 5 n 1 n+r = _ n [ 1 n _ r=0 ^ 5 n n n+r ] = & _ n [ 1 n _ r=0 ^ 5 n 1 1+(r / n) ] = & ₀^5 1 1+x d x=[ (1+x)]₀^5 = & 6- 1= 6 aligned

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