SOLUTION: Find the general formula for the sum of this series: 3+33+333+3333+... to n terms

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Question 1087090: Find the general formula for the sum of this series:
3+33+333+3333+... to n terms
Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!

Sn = 3+33+333+3333+... to n terms

If we multiply through by 3

3Sn = 9+99+999+9999+... to n terms

If we add 1 to each of the n terms on the right, we will 
have added n to both sides:

3Sn+n = 10+100+1000+10000+... to n terms

That is a geometric series with sum

 

So we have



Solve for Sn





Edwin
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