   Chapter 5, Problem 19P ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# Evaluate lim n → ∞ ( 1 n n + 1 + 1 n n + 2 + ⋯ + 1 n n + n ) .

To determine

To evaluate: The value of the function limn(1nn+1+1nn+2++1nn+n).

Explanation

Given information:

The function is limn(1nn+1+1nn+2++1nn+n).

Calculation:

Consider the function as follows:

y=limn(1nn+1+1nn+2++1nn+n) (1)

Find the value of the function as shown below.

Modify Equation (1).

y=limn1n(nn+1+nn+2++nn+n)=limn1n(nn+1+nn+2++nn+n)=limn1n(11+1n+11+2n++11+nn)=limn1n(11+1n+11+2n++11+1) (2)

Consider f(x)=11+x

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