5. Five mark example problems II

1. Find the rational form of the number \(0.6666...\)

 

Answer:

 

Rational form \(=\) $\frac{i}{i}$

 

 

2. Find the sum in \(n\) terms of the series \(5 + 55 + 555 + …\)

 

Answer:

 

The sum of the series \(=\) $\frac{i\left(i^i-i\right)}{i}-\frac{ii}{i}$

 

[Note: Enter the numbers and variables in separate boxes.]

 

 

3. Find the least positive integer \(n\) such that \(1 + 6 + 6^2 + … + 6^n > 5000\).

 

Answer:

 

The least positive integer \(=\)

 

 

4. A person saved money every year, but only half as much as he could have in the previous year. If he had totally saved \(₹7875\) in \(6\) years, then how much did he save in the first year?