Find the sum of the following series:
(i) 5 + 55 + 555 + … to n terms.
(ii) 7 + 77 + 777 + … to n terms.

Solution:

(i) to terms.
Let’s take 5 as a common term therefore we obtain,
terms
Now multiplying and dividing by 9 we obtain,
terms
terms

Therefore the G.P is

Using the formula,
The sum of GP for terms
Where,

(ii) to terms.
Let’s take 7 as a common term therefore we obtain,
Now multiplying and dividing by 9 we obtain,
terms
to terms
Therefore the terms are in G.P
Where,
Using the formula,
The sum of GP for terms