Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
NCTM or The Math Forum.



Re: Mathematical Induction
Posted:
Oct 9, 2012 5:15 PM



The sum is over the first n terms. The math before the ellipses shows how the pattern begins and after the ellipses shows how it ends. p(0)=2 p(1)=22*7 p(2)=22*7+2*7^2
(1(7)^(n+1))/4 + 2*(7)^n=(1+(81)(7)^(n+1))/4=(1(7)^(n+2))/4
Alternatively, prove by induction the formula for the sum of the first n term geometric progression, common ratio r and 0th term a, a(1r^n)/(1r). Then set a=2, r=7.
________________________________ From: Joe <discussions@mathforum.org> To: discretemath@mathforum.org Sent: Tuesday, 9 October 2012, 16:12 Subject: Mathematical Induction For the following problem:
22*7 + 2 * 7^2  ? + 2* (7)^n = (1(7)^n+1)/4
I understand that I need to first solve this for P(0). What I font understand is how the left side of the equation is equal to 2. Maybe I'm messing up the sequence of the equation or something but when I do the math I get:
(22*7 + 2 * 7^2) + (2* (7)^0) = 88
If I ignore the first portion and just do (2* (7)^0) I get 2. I am thinking maybe the math before the ellipses is just a example of a incrementing value of n and the math after the ellipses is the actual function p(). Is this correct?



