# How to find a general sum formula for the series: 5+55+555+5555+…..?

I have a question about finding the sum formula of n-th terms.

Here’s the series:

$5+55+555+5555$+……

What is the general formula to find the sum of n-th terms?

My attempts:

I think I need to separate 5 from this series such that:

$5(1+11+111+1111+....)$

Then, I think I need to make the statement in the parentheses into a easier sum:

$5(1+(10+1)+(100+10+1)+(1000+100+10+1)+.....)$

= $5(1*n+10*(n-1)+100*(n-2)+1000*(n-3)+....)$

Until the last statement, I don’t know how to go further. Is there any ideas to find the general solution from this series?

Thanks