Expert: Scott A Wilson - 1/17/2011

Question
Hello,

I'm not sure how I should write the equation since its got some symbols and stuff that I dont know how to type on here but here goes...

**infinity symbol* over *the weird E symbol* over *n=1** is all on the left side of the problem, like one on top of the other (but without a fraction line or something like that)... then there's 6(-3/5)^n  to the right of that

and that's it, the directions say to find the sum of the given series.

oh and it's multiple choice:
A) -9/4
B) 60/7
C) -9
D) 15

every time i worked it out something must have been wrong because i never got any of these options...so im not sure, am i plugging in some of the wrong numbers or something?

here's the equation i used: S = (a1)/(1-r)

and then i got (6)/(1-(-3/5)

and then that became 6/(8/5)

which is also 6*(5/8)

which is also 30/8

and simplified that's 15/4...

but thats not an option so i dont know now. what am i doing wrong?

thanks for any help you can give me!!

ps sorry if it's hard to understand how the equation looks, i hope it kind of makes sense

Answer
The definition given assumes the series starts with n = 0.
The problem starts with n = 1.
So this applies, but we have to subtract off the term n = 0.
The oth term is 6(-3/5)^0, which is just 6.

So, taking the 30/9, which is 15/4, and subtracting off 6, which is 24/4 gives
15/4 - 24/4 = -9/4, and that looks like A.