need a formula for this expression

$\displaystyle \frac{1^5 + 2^5 + 3^5 + ..... +(n-1)^5 + n^5}{1^4 + 2^4 + 3^4 + ..... + (n-1)^4 + n^4}$

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- Sep 1st 2010, 05:39 AMgrgrsanjayneed to derive a formula
need a formula for this expression

$\displaystyle \frac{1^5 + 2^5 + 3^5 + ..... +(n-1)^5 + n^5}{1^4 + 2^4 + 3^4 + ..... + (n-1)^4 + n^4}$ - Sep 1st 2010, 05:47 AMAckbeet
See here.

- Sep 1st 2010, 06:05 AMgrgrsanjay
$\displaystyle \frac{(2n^6 + 6n^5 +5n^4 - n^2)30}{(6n^5 + 15n^4 +10n^3 - n)12}$

i need derivation for this expression - Sep 1st 2010, 06:09 AMAckbeet
Right. Well, I would probably prove the numerator and denominator sums separately, using induction. Then you'd pretty much be done.

- Sep 1st 2010, 06:15 AMgrgrsanjay
- Sep 1st 2010, 06:42 AMSoroban
Hello, grgrsanjay!

What course are you taking?

These derivations are not difficult ,

. . but if we are limited to basic Algebra,

. . they will take*pages and pages!*

- Sep 1st 2010, 05:13 PMgrgrsanjay
oh OK anyway i got the answer

thank you guys :( - Sep 1st 2010, 05:20 PMAckbeet
Not exactly sure why you're frowning. If you got the answer on your own, that's the best result! That means you own the answer, and you'll understand the problem a lot better than if I were to simply show you the answer.