Let an be the sum of the first n triangular numbers, that

Chapter 11, Problem 36E

(choose chapter or problem)

Let \(a_{n}\) be the sum of the first n perfect squares, that is, \(a_{n}=\Sigma_{k=1}^{n} k^{2}\). Show that the sequence \(\left\{a_{n}\right\}\) satisfies the linear nonhomogeneous recurrence relation \(a_{n}=a_{n-1}+n^{2}\) and the initial condition \(a_{1}=1\). Use Theorem 6 to determine a formula for \(a_{n}\) by solving this recurrence relation

Equation Transcription:

Text Transcription:

a_n

a_n = the sum of k=1 to n k^2

{a_n}

a_n = a_n-1 + n^2

a_1 = 1