   Chapter 4.2, Problem 25E

Chapter
Section
Textbook Problem

Evaluating a Sum In Exercises 25-28, use the summation formulas to rewrite the expression without the summation notation. Use the result to find the sums for n = 10 , 100 , 1000 , and 10,000. ∑ i = 1 n 2 i + 1 n 2

To determine

To calculate: Sum of the expression i=1n2i+1n2 usingsummation formulas.

Explanation

Given: i=1n2i+1n2

Formula used: Formula for the sum of n natural number:

i=1ni=n(n+1)2

n times sum of constant is given as:

i=1nc=nc

Calculation: Consider the provided expression.

i=1n2i+1n2

To apply summation formula, split the expression in two parts:

i=1n2i+1n2=i=1n2in2+i=1n1n2

Factor out 2n2 from first summation and 1n2 from second summation:

i=1n2in2+i=1n1n2=2n2i=1ni+1n2i=1n1

Apply the formulas for summation:

i=1ni=n(n+1)2 and i=1nc=nc

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