Find the sum of the following series: `0. 5+0. 55+0. 555 to\ n\ t e r m s`

Explanation

`0.5+0.55+0.555+............nterms`

=`5{0.1+0.11+0.111+........} `

=`5/9​(9/10​+99/100​+999/1000​+..........)`

=`5/9​(1−1/10​+1−1/100​+1−1/1000​+....... n terms) `

=`5/9((1+1+1+....n)+(1/10+1/100
+1/100+....nterms))`

=`5/9​(n−(1/10​+1/100​+1/1000​+......... n terms)) `

Now, `1/10,1/100​,1/1000​ ,.... `
are in GP
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