Friday

August 22, 2014

August 22, 2014

Posted by **Jesse** on Thursday, June 10, 2010 at 12:33am.

(1)(2) + (2)(3) + ... n(n+1) =

n(n+1)(n+2)/3

complete the inductive step of its proof:

1(2) + 2(3) + ... k(k+1) + (k+1)(k+2)

I have no idea what to do.

- pre-calculus -
**Reiny**, Thursday, June 10, 2010 at 7:05amstep1

test for n=1

LS = (1)(2) = 2

RS = (1)(2)(3)/3 = 2, check!

step2

assume it is true for n=k, that is ...

(1)(2) + (2)(3) + ... k(k+1) =

k(k+1)(k+2)/3

step3

show that it must be true for n= k+1

that is ...

show

(1)(2) + (2)(3) + ... k(k+1) + (k+1)(k+2) =

(k+1)(k+2)(k+3)/3

LS = (1)(2) + (2)(3) + ... k(k+1) + (k+1)(k+2)

= [ (1)(2) + (2)(3) + ... k(k+1) ] + (k+1)(k+2)

= k(k+1)(k+2)/3 + (k+1)(k+2)

= k(k+1)(k+2)/3 + 3(k+1)(k+2)/3

= [ k(k+1)(k+2) + 3(k+1)(k+2) ]/3

= (k+1)(k+2) [k + 3]/3 , took out common factor

= (k+1)(k+2)(k+3)/3

= RS

**Related Questions**

Discrete Math - Theorem: For every integer n, if x and y are positive integers ...

pre-calculus - Prove 3+4+5+...+(n+2) = [n(n+5)]/2 for n>4 Do the first step ...

Mathematical induction. I'm stuck. So far I have.. - For all integers n ≥ ...

Pre Calc - find the magnitude and direction angle of the vector v, v=-2i+5j ...

Math - What is wrong with the following proof. You must explain your answer in ...

Calculus - Hi there i am having some problems trying to do my calculus homework...

Pre-Calculus - Can someone please help me with this problem? De Moivre’s theorem...

calculus - Find the cubic function f(x)=ax^3+bx^2+cx+d that has a local max ...

Pre-Calculus - I'm having a had time with this problem. Could you please help ...

communication - In general, thesis or central idea is supported by claims; ...