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Find the sum of the following series up ...

Find the sum of the following series up to n terms:(i) `5 + 55 + 555 + . . . . ` (ii) `. 6 +.66 +.666 +. . . . `

Text Solution

Verified by Experts

Let `S_n`= 5 + 55+ 555+... to n terms.
`S_n` =5(1+11+111+... to n terms)
`S_n` = `5/9`{(10−1)+(`10^2`−1)+(`10^3`−1)+...+(`10^n`−1)}
⇒`S_n`= `5/9`{(10+`10^2`+`10 ^3`+...+`10^n`)−n}
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