Find the summation for the series-: $$5+55+555+5555+...$$

I know it is a duplicate of this, but still, I am posting this because i was thinking of solving another way due to which I got stuck in another series.

My Attempt









So i think i got my answer.But i have doubt in summation of series-:


I got summation (from above ) as-: $=\frac{10}{9}*(\frac{10^{n+1}-10}{9}-n)$

But here , it is different .Which one is correct? I am stuck . Please help me out !

  • 3
    $\begingroup$ Your answer is correct. The second question you linked to only has answers that give you the $n^{th}$ term of the sequence $10, 110, \ldots$ $\endgroup$ – AnotherJohnDoe Oct 3 '17 at 8:09

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