Question

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 10 years ago

Answer 1

\[\sum_{n=m}^{k} ar ^{n}\]

Answer 2

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

Answer 3

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

Answer 4

@IrishBoy123

Answer 5

@IrishBoy123 mind helping?

Answer 6

for first n terms you have

\[\large \Sigma_{k=0}^{n-1} \ a \ r^k = a \frac{1-r^n}{1-r}\]

Answer 7

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)

Answer 8

so methodically plug into that formula and see where you go

Answer 9

ok thank you

Answer 10

ouch, you are using k and m in your problem so i have removed them to make it cleaner:

\[\large \Sigma_{i=0}^{n-1} \ a \ r^i = a \frac{1-r^n}{1-r}\]

Answer 11

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