Help me please!

[Solidjuss]

I am doing some university maths and need a bit help .... those two tasks:

1) [FONT=&quot](n^3 +5n) / 6 = ? I need to make a progression formula to here. For example 1*4+2*7+3*10+ ....n ( 3n+1 ) = n ( n+1 ) ^[/FONT][FONT=&quot] 2[/FONT] In my case, I got the right side and need to make the left one .
2) (4^[FONT=&quot]n[/FONT] +15n -1)/ 9 = ?
Same thing here Hope you know how to do it

Whoever is able to solve those, will be respected by me for whole my life
( I need to make up the formulas and than prove them with mathematical induction, but you can skip the induction part, just try to make up the formula)

 

[Davey Gaga]

[Moved] to the Study Hall.

 

[Aztec Triogal]

For arithmetic progression, don't you just have to lay out the equations in two ways and then add them to take out common factors? In other words, once you break it down, just copy/paste the same equation in reverse and then add the two equations. You'd get some 2X = ??? equation but the ??? would at least be clear of the successive number?

It's been a long time since I've done this sort of thing. Sorry bud.

 

[Solidjuss]

Probably not... I don't need to solve it... I need to make a formula that works for every natural number!
Thanks for helping anyway