Hey all,

can anyone show me how I can prove a statement like this by Induction. Thanks.

for all

Printable View

- Apr 11th 2011, 12:26 AMOilerProof by Induction
Hey all,

can anyone show me how I can prove a statement like this by Induction. Thanks.

for all - Apr 11th 2011, 12:35 AMveileen
Well, your n is natural unzero. (the sum starts with 1)

Read this: Mathematical induction - Wikipedia, the free encyclopedia

First step - verify if for n=1 that equality is true.

Second step (Induction) - we (you) suppose that k verify the equality and prove that then k+1 verify too. - Apr 23rd 2011, 10:32 PMOiler
Hey,

Stuck on the Induction step where I must rewrite the left-hand side..

..(1^3+2^3+3^3+...+n^3)+(n^3+1)=1/4*(n^3+1)(n^3+2)^2

EDIT: Should be (1^3+2^3+3^3+...+n^3)+(n+1)=1/4*(n+1)^2((n+1)+1)^2 and is straight forward to prove from there. Thanks for the help.. - Apr 24th 2011, 04:24 AMArchie Meade
- Apr 24th 2011, 08:40 AMProve It
Induction is not necessary...

http://i22.photobucket.com/albums/b3...sumofcubes.jpg - Apr 24th 2011, 03:58 PMArchie Meade
Unfortunately Prove It, as cool as it is, (Cool)

you get zero marks for answering the exam question

"Prove using induction that......." - Apr 24th 2011, 05:23 PMOiler
- Apr 24th 2011, 05:27 PMArchie Meade
Write the LHS as

(1/4)k^2(k+1)^2+(k+1)(k+1)^2

Then divide both sides by (k+1)^2 to get

(1/4)k^2+k+1 = (1/4)(k+2)^2 =(1/4)(k^2+4k+4)

QED.