ATAR Notes: Forum

Uni Stuff => Universities - Victoria => Monash University => Topic started by: blahh1234 on October 09, 2013, 02:30:13 pm

Title: MTH1030 Assignment 02 question help
Post by: blahh1234 on October 09, 2013, 02:30:13 pm: im currently doing mth1030 and i have an assignment due this week and i have no idea how to go about qu 3. any help would be greatly appreciated thanks!
Title: Re: MTH1030 Assignment 02 question help
Post by: TrueTears on October 10, 2013, 01:05:02 am: $\sum_{i=0}^n i^3 =\frac{n^2(n+1)^2}{4}= \frac{n^4}{4} + \frac{n^3}{2} + \frac{n^2}{4}$

$a = \frac{1}{4}, b = \frac{1}{2}, c = \frac{1}{4}, d=e=0$

I'll leave you to prove it using induction (very easy to do)
Title: Re: MTH1030 Assignment 02 question help
Post by: BigAl on October 10, 2013, 09:03:31 am: So they removed freaking apple logo question haha :)
Title: Re: MTH1030 Assignment 02 question help
Post by: blahh1234 on October 10, 2013, 09:37:22 am: Thanks! :)
Title: Re: MTH1030 Assignment 02 question help
Post by: kimk2kr on October 10, 2013, 02:32:35 pm: Quote from: TrueTears on October 10, 2013, 01:05:02 am
$\sum_{i=0}^n i^3 =\frac{n^2(n+1)^2}{4}= \frac{n^4}{4} + \frac{n^3}{2} + \frac{n^2}{4}$

$a = \frac{1}{4}, b = \frac{1}{2}, c = \frac{1}{4}, d=e=0$

I'll leave you to prove it using induction (very easy to do)

would you be able to explain this in tiny bit more detail please :) tyty
Title: Re: MTH1030 Assignment 02 question help
Post by: Devva[R] on October 10, 2013, 09:02:00 pm: All you're doing is finding values for $a,b,c,d$ and $e$ that satisfy the equation

$<br />an^4+bn^3+cn^2+dn+e = 1^3+2^3+3^3+...+n^3<br />$

You have five unknowns so have to set up a system of five equations to solve for $a,b,c,d$ and $e$