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the sum of the first n terms of the series 1/2+3/4+7/8+15/16+..... is equal to???

the sum of the first n terms of the series 1/2+3/4+7/8+15/16+..... is equal to???

Grade:12th pass

3 Answers

Shubham Sawarkar
22 Points
8 years ago
tn=(2n-1)/2n
  =1-1/2n
Sn=∑1-1/2n =n-∑1/2n (gp series)
    =n-1+2-n
Shivraj
17 Points
5 years ago
Sn=1/2 + 3/4 + 7/8 ........ n terms
    = (1- 1/2) + (1- 1/4) + ( 1 - 1/8 )...... n terms
=n -1/2[1-2--n]/1-1/2
n -1/2 ×2[1-2--n-n]
n-1+2--n
Kushagra Madhukar
askIITians Faculty 628 Points
3 years ago
Dear student,
Please find the solution to your problem.
 
tn = (2n – 1)/2n
   = 1 – 1/2n
Sn = ∑1 – 1/2n  = n – ∑1/2n (gp series)
     = n – 1 + 2-n
 
Thanks and regards,
Kushagra

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