📌 Example 1. Find the sum of the sequence 7, 77, 777, 7777, … to *n* terms.

✍ 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+⋯ to

*n*terms

📌 Ex2. Find the sum to *n* terms of the sequence, 8, 88, 888, 8888, …

✍ Solution:

The given sequence is 8, 88, 888, 8888, … . 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+⋯ to

*n*terms

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

(i) 5+55+555+⋯ (ii) .6+.66+.666+⋯

✍ Solution:

(i) 5+55+555+⋯

Let *S _{n}*=5+55+555+⋯ to

*n*terms

(ii) .6+.66+.666+…

Let *S _{n}*=06.+0.66+0.666+⋯ to

*n*terms

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