hello this is emily please help me ? :) my question is : find the formula for the nth partial sum Sn of each of the following series and use it to find the series' sum in case the series is convergent (5+ 5/3+ 5/9+5/27+…5/3^n-1)???

Question

goformit100 · Answer

|dw:1388090337162:dw|

anonymous · Answer

is this the final solution ?

goformit100 · Answer

yes, I think so.

anonymous · Answer

sorry , but how did u find it  ?

goformit100 · Answer

By summation method. the answer I wrote above is general equation.

anonymous · Answer

thank u sir

phi · Answer

Here are details on how to do this type of problem http://www.khanacademy.org/math/calculus/sequences_series_approx_calc/seq_series_review/v/geometric-series

anonymous · Answer

but they need to find the series's sum in case the series sum in case the series is convergent ?!

anonymous · Answer

Thank u mr phi i will check it now  ;)

agent0smith · Answer

If you factor out the 5, it's an infinite geometric series sum - remember how to find the sum of an inf. geometric series?

agent0smith · Answer

After factoring out the 5, first term is 1 and the common ratio would be 1/3.

anonymous · Answer

can i use the limit to find the sum

anonymous · Answer

?

anonymous · Answer

4+5/3+5/9+5/27+5/3^n