   Chapter 11.2, Problem 50E

Chapter
Section
Textbook Problem

# A sequence of terms is defined by a 1 = 1   a n = ( 5 − n ) a n − 1 Calculate ∑ n = 1 ∞ a n .

To determine

To calculate: The sum of the series.

Explanation

Given:

The sequence is an=(5n)an1. (1)

The first term of the sequence is a1=1.

Calculation:

Obtain the sum of the series.

Substitute 2 for n in equation (1),

a2=(52)a21=3a1

Substitute 1 for a1 in the above equation,

a2=31=3

Thus, the second term of the sequence is a2=3.

Substitute 3 for n in equation (1),

a3=(53)a31=2a2

Substitute 3 for a2 in the above equation,

a3=23=6

Thus, the third term of the sequence is a3=6.

Substitute 4 for n in equation (1),

a4=(54)a41=1a3=a3

Thus, the fourth term of the sequence is a4=6.

Substitute 5 for n in equation (1),

a5=(55)a51=0a4=0

Thus, the fifth term of the sequence is a5=0

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