Question

find the sum of series 5+55+555+...

Answer 1

nth term 
= 5 + 50 + 500 + ... + 5x10^(n-1) 
= 5 * [10^n - 1]/(10 - 1) 
= (5/9)[10^n - 1] 
Σ (5/9)[10^n - 1] 
= (5/9) [Σ10^n - Σ1] 
= (5/9) [10 * (10^n - 1)/(10 - 1) - n] 
= (5/9)[(10/9)*10^n - (10/9) - n] 
= (50/81) * (10^n - 1) - 5n/9.


hope this helps you....

Answer 2

Answer:

Step-by-step explanation:

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