7. Five marks exercise problems III

1. Find the sum of the geometric series \(3 + 6 + 12 + … + 1536\).

 

Answer:

 

The sum of the geometric series \(=\)

 

 

2. Kumar writes a letter to four of his friends. He asks each one of them to copy the letter and mail it to four different people with the instruction that they continue the process similarly. Assuming that the process is unaltered and it costs \(₹2\) to mail one letter, find the amount spent on postage when \(8^{\text{th}}\) set of letters is mailed.

 

The amount spent on postage \(=\) \(₹\)

 

 

3. Find the rational form of the number \(0.\overline{123}\).

 

 

The rational form \(=\) $\frac{i}{i}$

 

[Note: Enter the simplest form]