Identify whether the series is a convergent or divergent geometric series and find the sum, if possible.

Question

anonymous · Answer

attachment

anonymous · Answer

@dan815

anonymous · Answer

@Jonathan1997

anonymous · Answer

This is a convergent geometric series. The sum is 48.

 This is a divergent geometric series. The sum is 48.

 This is a convergent geometric series. The sum cannot be found.

 This is a divergent geometric series. The sum cannot be found.

Almost Forgot this

perl · Answer

its convergent because its a geometric series, r = 5/6

anonymous · Answer

ok so now i just need to find the sum if there is one.

anonymous · Answer

so number 3 right

perl · Answer

if the sum is convergent , and can be found

perl · Answer

the sum is convergent and can be found. the sum is 48

anonymous · Answer

wait i fail

anonymous · Answer

I know the answer

anonymous · Answer

summation of 8(5/6)^(I-1) from i=1 to infinity

anonymous · Answer

http://www.wolframalpha.com/input/?i=summation+of+8%285%2F6%29%5E%28I-1%29+from+i%3D1+to+infinity

phi · Answer

See https://en.wikipedia.org/wiki/Geometric_series#Formula which shows the formula and a derivation if you are interested

phi · Answer

notice in wolfram.. you have to read the fine print.  wolf is assuming i stands for sqr(-1).  if you used k for the index, you would get the correct answer.

anonymous · Answer

@phi 
so my answer was wrong?

phi · Answer

what was your answer ?

anonymous · Answer

This is a divergent geometric series. The sum cannot be found.

perl · Answer

the sum is convergent and can be found. the sum is 48

perl · Answer

its a geometric series , |r|<1

anonymous · Answer

http://www.wolframalpha.com/input/?i=summation+of+8%285%2F6%29%5E%28I-1%29+from+i%3D1+to+infinity according to this it is divergent and the sum cannot be found

phi · Answer

it is convergent, so you are incorrect.

if you get a calculator and find (5/6)^2  and (5/6)^3, and so on... you will see that when n is very big  (5/6)^n  is getting closer and closer to 0

anonymous · Answer

okay but can the sum be found?

phi · Answer

Help - re-read my post up above more carefully

perl · Answer

oh sorry, nevermind. help, you inputted wrong

perl · Answer

help, this is correct input http://www.wolframalpha.com/input/?i=summation+of+8%285%2F6%29^%28i-1%29+from+i%3D1+to+infinity

anonymous · Answer

Thank you very much

perl · Answer

help you used I and i, can't change the letter

anonymous · Answer

ok

perl · Answer

phi, do you have any experience with maple syntax

phi · Answer

@perl  re: maple, not enough to be helpful