A few days ago
Sequence and Series?
Determine whether the sum(0- infinity) of (1+2^n+3^n)/(5^n) converges or diverges. If it converges find the sum.
Top 1 Answers
A few days ago
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Dividing Nr and Dr by 5^n, the series becomes
sum (0 – inf) of (1/5)^n)+(2/5)^n+(3/5)^n
take each term separately; each is a Geometric progression
Term 1 sum = 1+ 1/5+ 1/25+…….to infinity = 1/(1-1/5) = 5/4
Term 2 sum = 1+2/5+4/25+….. = 1/(1-2/5) = 5/3
Term 3 sum = 1+(3/5)+(9/25)+…. = 1/(1-3/5) = 5/2
The answer converges to 5/4+5/3+5/2 = (15+20+30)/12
= 65/12 …ANSWER
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