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Find the sum of the following series : ...

Find the sum of the following series : `0. 7+0. 77+0. 777+ ton` terms

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`S_n=7+77+777+7777+...........n`
`= 7/9​ [9+99+999......n]`
`= 7/9​ [(10−1)+(100−1)+(1000−1) +.........n ]`
`=7/9​ [10+100+1000 + ... n- (1+1+1+1+......... n)`
...
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