SOLUTION: find the sum of the series 5/13 + 55/(13)^2 + 555/(13)^3 + ...

Question 328453: find the sum of the series 5/13 + 55/(13)^2 + 555/(13)^3 + ...
Answer by galactus(183) (Show Source): You can put this solution on YOUR website!
This is kind of tricky trying to set up a general form for 5,55,555,....
We can think of the numerators: 5,55,555,5555,...., as

But, this gives us a general form of

Using the formula for the sum of an infinite series we get

The sum is 65/36
RELATED QUESTIONS
Find the sum of the following arithmetic series 5+9+13+17+......41 The sum of this... (answered by Big Poop)

Find the sum of each of these series using the series formula. a) -11 - 3 + 5 + 13 +... (answered by ikleyn)

find the indicated sum for each arithmetic series S15 for 5 + 9 + 13 +... (answered by josgarithmetic)

find the sum of the 1st 13 terms of the series... (answered by Edwin McCravy)

Find the sum of n term of the series. 1+4+13+40+........... (answered by KMST)

Find the exact value of cos(t/2) if {{{ tan(t)=12/5 }}} and {{{ pi (answered by MathLover1)
Find the sum of series 1+4+13+40+121 to n terms (answered by MathLover1)
Find the value of the series... (answered by Fombitz,MathLover1)
Find the sum of 1/2(4) +1/3(5) + 1/4(6) + ..... + 1/13(15) (answered by greenestamps,ikleyn)