How to find the sum of the infinite geometric series 0.9 + 0.09 + 0.009 +…?

Maui1opj

Maui1opj

Answered question

2023-03-22

How to find the sum of the infinite geometric series 0.9 + 0.09 + 0.009 +…?

Answer & Explanation

srnessgebf

srnessgebf

Beginner2023-03-23Added 8 answers

For instance:
1 3 = 0 . 3 ¯
3 × 1 3 = 0 . 9 ¯ but is also equal to 1, Consequently, both numbers are equal.
Drake Peters

Drake Peters

Beginner2023-03-24Added 5 answers

The other response is accurate, but it's also important to note how using the geometric series formula would produce the outcome:
For | r | < 1 and a 0 we have n = 0 r n = a 1 - r
Applying this, as | 1 10 | < 1 , we have
0.9 + 0.09 + 0.009 + ... = n = 0 9 10 ( 1 10 ) n
= 9 10 1 - 1 10
= 9 10 9 10
= 1

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