## anonymous one year ago 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<k find a formula for evaluating the sum.

1. anonymous

$\sum_{n=m}^{k} ar ^{n}$

2. anonymous

$S(n) = \frac{ a _{1}(1-r) }{ 1-r }$

3. anonymous

i know this formula will drive the same way this formula did ^ but just dont know how to set up ?

4. anonymous

@IrishBoy123

5. anonymous

@IrishBoy123 mind helping?

6. IrishBoy123

for first n terms you have $\large \Sigma_{k=0}^{n-1} \ a \ r^k = a \frac{1-r^n}{1-r}$

7. 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)

8. IrishBoy123

so methodically plug into that formula and see where you go

9. anonymous

ok thank you

10. IrishBoy123

ouch, you are using k and m in your problem so i have removed them to make it cleaner: $\large \Sigma_{i=0}^{n-1} \ a \ r^i = a \frac{1-r^n}{1-r}$

11. IrishBoy123

i mean......i have replaced the k by i