π Example 1. Find the sum of the sequence 7, 77, 777, 7777, β¦ to *n* terms.

β Solution: This is not a geometric sequence, however, we can relate it to a geometric sequence. by writing the terms as

*S _{n}*=7+77+777+7777+β― to

*n*terms

π Ex2. Find the sum to *n* terms of the sequence, 8, 88, 888, 8888, β¦

β Solution:

The given sequence is 8, 88, 888, 8888, β¦ . This sequence is not a geometric sequence. However, it can be changed to geometric sequence. by writing the terms as

*S _{n}*=8+88+888+8888+β― to

*n*terms

π Ex3. Find the sum of the following series up to *n* terms:

(i) 5+55+555+β― (ii) .6+.66+.666+β―

β Solution:

(i) 5+55+555+β―

Let *S _{n}*=5+55+555+β― to

*n*terms

(ii) .6+.66+.666+β¦

Let *S _{n}*=06.+0.66+0.666+β― to

*n*terms

π Let’s read post β’Writing a Repeating Decimal as a Fraction with three methodsπ.