Question

Calculate the sum of the series

Answer 1

\[\sum_{i=3}^{8}(1/2)^i\]

Answer 2

\[\sum_{i=3}^{8}(1/2)^i=(1/2)^3+(1/2)^4+(1/2)^5+(1/2)^6+(1/2)^7+(1/2)^8\]

Answer 3

You can easily solve it by Geometric Progression:

\[\frac{1}{8} + \frac{1}{16} + \frac{1}{32} .......................+ \frac{1}{256}\]

Here:

\[a = \frac{1}{8}\]

\[r = \frac{1}{2}\]
and \(n = 6\)

Use the Sum formula for G.P.:

\[\large Sum = \frac{a(1-r^n)}{1 - r}\]