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The sum of the first 20 terms of the series 3/2+5/4+9/8+17/16+........ is equal to?

The sum of the first 20 terms of the series 3/2+5/4+9/8+17/16+........ is equal to?
 

Grade:12th pass

1 Answers

Agrata Singh
208 Points
5 years ago
Clearly nth term is
Tn=(2n+1)/2n=1+(1/2n)=1+(1/2)n
Sum S=∑Tn= ∑(1+(1/2)n)=∑1+∑(1/2)n
20+(Sum of GP with first term ½ and common ratio 1/2)
20+[1/2{1-(1/2)20}/(1-1/2)]
20+(1-(1/2)20)
21-(1/2)20
~21 as (1/2)20 is very small
 
Hope this helps you 

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