Explanation Given: a n = a n − 1 + n 2 , a 1 = 1 … i Formula used: Calculation: Now the characteristic equation of ( i ) is x − 1 = 0 ⇒ g e n e r a l s o l u t i o n i s c .1 n = c … i i The particular solution for n 2 is of the form α n + β n 2 + γ n 3 Substituting this in ( i ), we obtain α n + β n 2 + γ n 3 − ( α ( n − 1 ) + β ( n − 1 ) 2 + γ ( n − 1 ) 3 ) = n 2 Putting the values for n and simplifying, we obtain the equations α + β + γ = 1<

Discrete Mathematics and Its Applications ( 8th International Edition ) ISBN:9781260091991

8th Edition

ISBN: 9781259676512

Author: Kenneth H Rosen

Publisher: McGraw-Hill Education

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence. It was invented by German mathematician Carl Friedrich Gauss.

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Chapter 8.2, Problem 36E

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Find the formula for ∑1nk2, by solving the recurrence equation an=an−1+n2, a1=1

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Chapter 8.2, Problem 35E

Chapter 8.2, Problem 37E

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Chapter 8 Solutions

Discrete Mathematics and Its Applications ( 8th International Edition ) ISBN:9781260091991

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Find the formula for ∑ 1 n k 2 , by solving the recurrence equation a n = a n − 1 + n 2 , a 1 = 1

Solution Summary: The author explains how to solve the recurrence equation for n2 by putting the values for n and simplifying.

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Find the formula for ∑1nk2, by solving the recurrence equation an=an−1+n2, a1=1

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