Geometric series problem..

Question

anonymous · Answer

attachment

anonymous · Answer

its saying the correct answer is 0.09090909 but I'm not sure how they get to that answer..

superdavesuper · Answer

can u show what u have done so far?

anonymous · Answer

I'm not sure how to start it

superdavesuper · Answer

u know geometric series right? i will provide a hint that should get u started...

anonymous · Answer

ok thanks

anonymous · Answer

so i know you take the n power out and raise it to the n. but in this case we have n-1

anonymous · Answer

thats where i get confused

superdavesuper · Answer

$$\sum_{n=1}^{\infty}\frac{ (-2)^{n-1} }{ 9^{n} } = \sum_{n=1}^{\infty}\frac{1}{-2}(\frac{ -2}{ 9})^n$$

superdavesuper · Answer

yes, the n-1 is a problem but the above should help :)

anonymous · Answer

ok thanks! but how did you get the 1/-2?

superdavesuper · Answer

multiply the above n bottom by -2/-2 :D

anonymous · Answer

hmm when i do that i get 4..

anonymous · Answer

sorry I'm just very confused. but thank you anyway!

superdavesuper · Answer

do u understand the hint? show me where u get confused n may be i can help :)

anonymous · Answer

i don't know what you multiple 2/2 with? because when i multiply 2/2 i get 4/18..

superdavesuper · Answer

i multiple the top n bottom by -2/-2 so that (-2)^(n-1) becomes (-2)^n. read the hint again n see if u can understand that plz

anonymous · Answer

ok i will thank you

superdavesuper · Answer

good luck! i think once u understand the hint, u should be able to calculate the ans :)