Summation General Formula

[Alphonse]

Sum of ((4^k+5^(2k))/(63k)) from 1 to n

The above problem was given as a homework problem and WolframAlpha gave that solution which I think is in the wrong form according to my Professor's class structure. Could somebody please help me with identifying where to apply certain formulas?

Ignore the picture below.

 

[MarkFL]

Are you certain the following isn't intended?

\(\displaystyle \displaystyle S= \sum_{k=1}^{n}\left(\frac{4^k+ 5^{2k}}{63^k}\right)\)

 

[Alphonse]

I was thinking that but what if it wasn't? The function being a typo would make the problem a lot easier but I'm not sure if it is or not, if it's not then what if I don't know how to do the problem? Is this sort of problem something not typically found or is it just a difficult problem?

 

[MarkFL]

I was thinking that but what if it wasn't? The function being a typo would make the problem a lot easier but I'm not sure if it is or not, if it's not then what if I don't know how to do the problem? Is this sort of problem something not typically found or is it just a difficult problem?

What you gave in 2 of the 3 instances in your OP, that is:

\(\displaystyle \displaystyle S= \sum_{k=1}^{n}\left(\frac{4^k+ 5^{2k}}{63k}\right)\)

I wouldn't know how to do offhand, and would have to consult a summation guru I know. What I gave, I can do...