Expert: Sherman D. - 4/12/2008

Question
Hi, I have an upcoming Math exam (I'm in college) but i can't seem to understand math inductions. please show me how, thanks!

Prove by mathematical induction that n=1 and n=k:

4+8+12+...+4n= 2n(n+1)

Answer
4,8,12,...,4n

an = a1 + d(n - 1)

a(2) = 4 + d(2 - 1)
8 = 4 + d
d = 4

a(3) = 4 + d(3 - 1)
12 = 4 + 2d
8 = 2d
d = 4

an = 4 + 4(n - 1)
an = 4(1 + n - 1)
an = 4n

Sn = (n/2)(a1 + an)
Sn = (n/2)(4 + 4n)
Sn = 4(n/2)(1 + n)
Sn = 2n(n + 1)

You can find all the info you need to get your problem proven.

www.ltcconline.net/greenl/Courses/103B/seqSeries/ARITSEQ.HTM

the work i did at the time was to show you how they got what they got.