How do you find the sum of the finite geometric sequence of #sum_(i=0)^10 5(-1/3)^(i-1)#?

1 Answer
May 30, 2018

Answer:

#S = 5(-1/3)^{-1}( {1 - (-1/3)^{11})/(1 - (-1/3)) ) = -221435/19683#

Explanation:

The #n# term finite geometric series that starts with 1 has a straightforward sum:

#S_n = sum_{k=0}^{n-1} r^k = {1 - r^n}/{1-r}#

For the general geometric series we multiply by the first term. Our series has 11 terms.

#S = sum_{i=0}^{10} 5 (-1/3) ^(i-1)#

#S = 5(-1/3)^{-1}( {1 - (-1/3)^{11})/(1 - (-1/3)) )#

#S = -221435/19683#