How do I find the sum of the geometric series 8 + 4 + 2 + 1?

1 Answer
MrsRudolph221
Sep 24, 2014

Now, this is called a finite sum, because there are a countable set of terms to be added. The first term, #a_1=8# and the common ratio is #1/2# or .5. The sum is calculated by finding: #S_n= frac{a_1(1-R^n)}{(1-r)# = #frac{8(1-(1/2)^4)}\(1-1/2)# = #frac{8(1-1/16)}{1-(1/2)}# =#8frac{(15/16)}{1/2}# = #(8/1)(15/16)(2/1)# = 15.

It is interesting to note that the formula works the opposite way, too:
#(a_1(r^n-1))/(r-1)#. Try it on a different problem!

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