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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

Calculate k = 1 8 ( k 2 + 1 ) .

To determine

To calculate: The value of the expression is k=18(k2+1).

Answer

Solution:

The value of the expression k=18(k2+1) is 212.

Explanation

Given Information:

The provided expression is k=18(k2+1).

Formula Used:

The sum of n numbers x1, x2, x3,,xn is given by

k=1nxk=x1+x2++xn

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

k=1n1=n

The sum of the square of first n natural numbers,

k=1nk2=n(n+1)(2n+1)6

Calculation:

Consider the sum k=18(k2+1).

Separate the components of the expression as follows:

k=18(k2+1)=k=18(k2)+k=18(1)

Apply the formula for the summation of the expressions,

Firstly, the sum of the first expression is:

k=1n(k2)=k(k+1)(2k+1)6k=18(k2)=8(9)(17)6=204

Secondly, the sum of the second expression is:

k=1n(1)=n.1k=18(1)=8.1=8

Add both the values for the expressions:

k=18(k2+1)=k=18(k2)+k=18(1)=204+8=212

Hence, the value of the expression k=18(k2+1) is 212.

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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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