# Thread: Evaluate sum to 'n' terms(Sequences and Series)?

1. ## Evaluate sum to 'n' terms(Sequences and Series)?

Evaluate sum of n terms of the series:

$\displaystyle \frac{8}{5} + \frac{16}{65} + \frac{24}{325} + \mbox{... till n terms}$

2. Hello,
Originally Posted by fardeen_gen
Evaluate sum of n terms of the series:

$\displaystyle \frac{8}{5} + \frac{16}{65} + \frac{24}{325} + \mbox{... till n terms}$
So the numerator is 8n, but the denominator ??

5
5x13
5x5x13

what's the pattern ? is it possible to get more terms ?

3. I do not know Does anybody see the trick?

4. Okay, one possibility would be $\displaystyle 5^{\lfloor \frac{n+1}{2}\rfloor}13^{\lfloor \frac n2\rfloor}$

so then you can make the difference between odd and even terms...

5. Originally Posted by Moo
Okay, one possibility would be $\displaystyle 5^{\lfloor \frac{n+1}{2}\rfloor}13^{\lfloor \frac n2\rfloor}$

so then you can make the difference between odd and even terms...
Difference between odd and even terms? Could you explain?

6. Originally Posted by fardeen_gen
Difference between odd and even terms? Could you explain?
Vocabulary problem I meant separate.

The even terms in the form 2k will be $\displaystyle 5^k13^k$
The odd terms in the form 2k+1 will be $\displaystyle 5^{k+1}13^k$

Then, I guess you'll have a different result, depending on whether n is odd or even.
I don't see a shortcut for the moment. And it doesn't look nice