is 3 +, 20- 37 1 (-1)" n=0 years old. How old am 1?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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X is 3 + 20
years old. How old am 1?
n=0
37 1
Transcribed Image Text:X is 3 + 20 years old. How old am 1? n=0 37 1
Expert Solution
Step 1

Given the age of the person is 3+n=020(-1)n3n-1 years old.

Evaluation of summation term:

20n=0-1n3n-120n=0-1n3n.3-120n=03-1n3n60n=0-1n3n60n=0-13nn=0-13n is an infinite geometric series with first term a=1 and common ratio r=-13.By ratio test it is convergent.The sum S=a1-rS=11+13=34Hence, n=0-13n=34Therefore, n=060-13n=60×34=45.

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