anonymous
  • anonymous
hey guys hope your well ! so I have this evaluating proof problem ,can anyone help me plzzz. Its geometric series , question is : suppose m and k are integers with m
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
\[\sum_{n=m}^{k} ar ^{n}\]
anonymous
  • anonymous
\[S(n) = \frac{ a _{1}(1-r) }{ 1-r }\]
anonymous
  • anonymous
i know this formula will drive the same way this formula did ^ but just dont know how to set up ?

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anonymous
  • anonymous
anonymous
  • anonymous
@IrishBoy123 mind helping?
IrishBoy123
  • IrishBoy123
for first n terms you have \[\large \Sigma_{k=0}^{n-1} \ a \ r^k = a \frac{1-r^n}{1-r}\]
IrishBoy123
  • IrishBoy123
so you can calculate 2 summations, each starting at zero and ending somewhere that leaves you with the interval you want to sum over a bit like S(8 to 10) = S(10) - S(7)
IrishBoy123
  • IrishBoy123
so methodically plug into that formula and see where you go
anonymous
  • anonymous
ok thank you
IrishBoy123
  • IrishBoy123
ouch, you are using k and m in your problem so i have removed them to make it cleaner: \[\large \Sigma_{i=0}^{n-1} \ a \ r^i = a \frac{1-r^n}{1-r}\]
IrishBoy123
  • IrishBoy123
i mean......i have replaced the k by i

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