Find-the-sum-of-the-nth-term-of-the-series-1-2-3-4-7-8-15-16-

Question Number 46461 by Tawa1 last updated on 26/Oct/18

Find the sum of the nth term of the series : \frac{1}{2} + \frac{3}{4} + \frac{7}{8} + \frac{15}{16} + \dots

Answered by tanmay.chaudhury50@gmail.com last updated on 26/Oct/18

S_{n} = 1 - \frac{1}{2} + 1 - \frac{1}{2^{2}} + 1 - \frac{1}{2^{3}} + 1 - \frac{1}{2^{4}} + \dots

S_{n} = (1 + 1 + 1 \dots) - (\frac{1}{2} + \frac{1}{2^{2}} + \frac{1}{2^{3}} + \dots)

S_{n} = n - {\frac{1}{2} (\frac{1 - \frac{1}{2^{n}}}{1 - \frac{1}{2}})}

S_{n} = n - 1 + \frac{1}{2^{n}}

Commented by Tawa1 last updated on 26/Oct/18

God bless you sir

Facebook Tweet Pin