**Example of Geometric Progression**

** Test Your Skills **

**Question : **

Given A = 2^{65}

B = 2^{65} + 2^{65} + 2^{65} +….+ 2^{65}

Find out which is larger-A or B?

**Solve :**

To find out the solution, first of all we need to sum up all the terms given in â€˜Bâ€™.

All the terms, given in a series, is in Geometric Progression (G.P.)

The series can be written as:

B = 2^{0},…, 2^{62}, 2^{63}, 2^{64}

Here, a = 2^{0} = 2

r = 2

n = 65

Sn = [a (r^{n}-1)] / (r – 1)

= 2^{0} (2^{65}-1) / (2-1)

= 1 (2^{65}-1) / 1

B = 2^{65}-1

We already know that A = 2^{65}

A is thus larger than B.

Answers | ||||
---|---|---|---|---|

A) 67 | (B) 0 |