Find the sum of the series

Question

mony01 · Answer

$$\sum_{n=1}^{\infty}\frac{ 6 }{ n ^{6} }$$

hartnn · Answer

do you realize 6/n^6 is n'th term of an GEOMETRIC series ?

hartnn · Answer

what is a = 1st term = ..?
what is common ratio = r = ..?

then Sum of this series is just 
$\Large S_n = \dfrac{a}{1-r}$

hartnn · Answer

to get a = 1st term, plug in n=1

mony01 · Answer

but it says rounded of to the 3 decimal places

anonymous · Answer

isn't a geometric supposed to be something like 6/(6^n) ?

hartnn · Answer

yes, scratch that....it isn't geometric

hartnn · Answer

this problem belongs to which topic ? any similar problems ?

anonymous · Answer

anonymous · Answer

6.104 if you round to 3 decimal places

mony01 · Answer

you guys dont know how to get that?

hartnn · Answer

i might have came across such problems b4, but i nned to refresh what method was used....

anonymous · Answer

I'm not at that level yet >.<

kainui · Answer

hartnn · Answer

is this fourier series topic ?

kainui · Answer

Partially, although I think for the most part it's really just a clever use of power series. Here's a similar example: http://en.wikipedia.org/wiki/Basel_problem