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in the chapter series and sequence following is the question: Find the sum of 1 + 2/2 + 3/2 2 + 4/2 3 + …. to n terms

in the chapter series and sequence following is the question: Find the sum of 1 + 2/2 + 3/22 + 4/23 + …. to n terms

Grade:12th pass

1 Answers

Vikas TU
14149 Points
4 years ago
Dear student 
S =  1 + 2/2 + 3/22 + 4/23 + …. to n/(2n-1) terms..................1
S/2 = 1/2 + 2/22 + 3/23 + 4/24 + …. to n/2n terms.....................2 
Subtract 1 – 2 
S – S/2 = 1+ ½ + 1/22 + ….............. 1/2n-1  + n/2n
This is GP. 
Put the sum of GP formula 
S/2 = 2(2n – 1) / 2n + n/ 2n 
S = 4 – 2/2n  (n+2)
 
 
 

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