Friday

August 29, 2014

August 29, 2014

Posted by **A-A** on Thursday, February 17, 2011 at 2:42am.

using the mathematical induction.

please help..

- math induction -
**MathMate**, Thursday, February 17, 2011 at 9:10am1(2)+2(3)+3(4)+...+n(n+1)= n(n+1)(n+2)/

**3**

(Note: The denominator is 3, not 2)

Basis: n=1

1(2)=2

1(2)(3)/3=2

n=1 is valid.

Assume:

1(2)+2(3)+3(4)+...+k(k+1)= k(k+1)(k+2)/3

is valid for k=n

then try to prove that the relation is valid for k=n+1.

1(2)+2(3)+3(4)+...+n(n+1) + (n+1)(n+2)

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

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

= ( n^3+6*n^2+11*n+6 )/3

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

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

which means that the expression is valid also for n+1. QED

**Related Questions**

advance algebra - 2(2^1) +3(2^2) + 4(2^3)+...+n^3 = [n(n+1)/2]^2 using the ...

mathematical induction - solve this using the mathematical induction : 1/1(3)+1/...

Calculus - Use mathematical induction to prove that the statement holds for all ...

math - how do you prove that (a-1) divides ((a^n)-1) evenly using mathematical ...

AP Calc - Use mathematical induction to prove that the statement holds for all ...

Algebra - Prove by mathematical induction that 3^(3n+1) + 2^(n+1) is divisible ...

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

Math - Mathematical Induction - 3. Prove by induction that∑_(r=1)^n▒...

math - Can anyone please help me with the following question: Prove by ...

proof by mathematical induction - subject is PreCalulus. 2^(k+3) = and < (k+3...