The sum of the first n terms of the series:

1/2 + 3/4 + 7/8 + 15/16 + ....... is?

Please help me in working out this problem.

The given sequence is, 
1/2 + 3/4 + 7/8 + 15/16 + ......n terms
We can write each individual as, 12=1-12, 34=1-14, 78=1-18 and .......till n terms.Now writing each term in its new form we get, 1-12+1-14+1-18+.......+1-12n=(1 +1+1+1+...+1)-12-14-18-.......-12n=n-12+14+18+.......+12n.....(1)Now 12+14+18+.......+12n is a GP with common ratio=12 so ,  12+14+18+.......+12n=121-12n1-12 =1-12nPutting this value in equation (1) we get, n-12+14+18+.......+12n=n-1-12n

 

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