Tuesday

March 3, 2015

March 3, 2015

Posted by **Josh** on Friday, July 29, 2011 at 4:29pm.

2 + 6 + 10 + . . . + (4n – 2) = 2n^2

is true

- Math -
**Damon**, Friday, July 29, 2011 at 5:38pmn an sum n

1 2 2

2 6 8

3 10 18

4 14 32

n (4n-2) 2n^2

(n+1) (4(n+1)-2) [2n^2+ (4(n+1)-2)] or hopefully 2(n+1)^2

[2n^2+ (4(n+1)-2)] = 2n^2+4n +2

and

2(n+1)^2 = 2(n^2+2n+1) = 2n^2+4n+2 done

2n^2+ (4(n+1)-2)

- Math -
**Reiny**, Friday, July 29, 2011 at 5:46pmUsing the 3 step process:

1. test for n=1

LS = 2

RS = 2(1^2) = 2

2. assume it true for n=k

that is ....

2+4+6 + ... + (4k-2) = 2k^2

3 . prove it is then true for =k+1

or

2+4+6+ ... + (4k-2) + 4(k+1)-2 = 2(k+1)2

LS = [2+4+6+...+ 4k-2 ] + 4(k+1)-2

= 2k^2 + 4k + 4 - 2

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

= 2(k+1)^2

= RS

QED

**Answer this Question**

**Related Questions**

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

Algebra II - In an induction proof of the statement 4+7+10+...+(3n-1)=n(3n+5)/2 ...

math - 1)Find the third iterate x3 of f(x)=x2-4 for an initial value of x0=2 A)-...

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

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

math - Use mathematical induction to show that 3n + 7n − 2 is divisible by...

math induction - prove the product of 4 consecutive integers is always divisible...

Math - 1. Determine the formula for the nth term of the following sequence: 6, ...

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

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