Some Series of Recurring Digit Numbers

📌 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
Sn=7+77+777+7777+⋯ to n terms

a series of recurring digit numbers a

📌 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
Sn=8+88+888+8888+⋯ to n terms

a series of recurring digit numbers b

📌 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 Sn=5+55+555+⋯ to n terms

a series of recurring digit numbers d

(ii) .6+.66+.666+…
Let Sn=06.+0.66+0.666+⋯ to n terms

a series of recurring digit numbers c

💎 Let’s read post 👉Writing a Repeating Decimal as a Fraction with three methods👈.

RELATED POSTs