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Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

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BuyFindarrow_forward

Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

In Problems 20-25, use the sum formulas I-V to express each of the following without the summation symbol. In Problems 20-23, find the numerical value.

25.   i = 1 n ( 1 2 i n + i 2 n 2 ) ( 3 n )

To determine

To calculate: The expression of i=1n(12in+i2n2)(3n) without the summation symbol.

Explanation

Given Information:

The provided sum is i=1n(12in+i2n2)(3n).

Formula used:

The value of the sum k=1n(xk±yk)=k=1nxk±k=1nyk.

The value of the sum k=1nk=n(n+1)2.

The value of the sum k=1n1=n.

The value of the sum k=1ncxk=ck=1nxk.

The value of the sum k=1nk2=n(n+1)(2n+1)6.

Calculation:

Consider the sum i=1n(12in+i2n2)(3n).

This can be written as,

i=1n(12in+i2n2)(3n)=i=1n(3n3n2in+3ni2n2)=i=1n(3n6in2+3i2n3)

Recall that the value of the sum k=1n(xk±yk)=k=1nxk±k=1nyk.

Thus,

i=1n(12in+i2n2)(3n)=i=1n(3n6in2+3i2n3)=i=1n3ni=1n(6in2)+i=1n(3i2n3)

Recall that the value of the sum k=1ncxk=ck=1nxk.

Thus,

i=1n(12in+i2n2)(3n)=i=1n3ni=1n(6in2)+i=1n(3i2n3)=3ni=1n16n2i=1ni+3n3i=1ni2

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Chapter 13 Solutions

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Sect-13.1 P-9ESect-13.1 P-10ESect-13.1 P-11ESect-13.1 P-12ESect-13.1 P-13ESect-13.1 P-14ESect-13.1 P-15ESect-13.1 P-16ESect-13.1 P-17ESect-13.1 P-18ESect-13.1 P-19ESect-13.1 P-20ESect-13.1 P-21ESect-13.1 P-22ESect-13.1 P-23ESect-13.1 P-24ESect-13.1 P-25ESect-13.1 P-26ESect-13.1 P-27ESect-13.1 P-28ESect-13.1 P-29ESect-13.1 P-30ESect-13.1 P-31ESect-13.1 P-32ESect-13.1 P-33ESect-13.1 P-34ESect-13.1 P-35ESect-13.1 P-36ESect-13.1 P-37ESect-13.1 P-38ESect-13.1 P-39ESect-13.1 P-40ESect-13.2 P-1CPSect-13.2 P-2CPSect-13.2 P-1ESect-13.2 P-2ESect-13.2 P-3ESect-13.2 P-4ESect-13.2 P-5ESect-13.2 P-6ESect-13.2 P-9ESect-13.2 P-10ESect-13.2 P-11ESect-13.2 P-12ESect-13.2 P-7ESect-13.2 P-8ESect-13.2 P-23ESect-13.2 P-24ESect-13.2 P-13ESect-13.2 P-14ESect-13.2 P-15ESect-13.2 P-16ESect-13.2 P-17ESect-13.2 P-18ESect-13.2 P-19ESect-13.2 P-20ESect-13.2 P-21ESect-13.2 P-22ESect-13.2 P-25ESect-13.2 P-26ESect-13.2 P-27ESect-13.2 P-28ESect-13.2 P-29ESect-13.2 P-30ESect-13.2 P-31ESect-13.2 P-32ESect-13.2 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