S(n): 2+7+12+...+(5n+2) = 1/2(n+1)(5n+4)
S(1): LHS (5(1)+2) = 9
RHS 1/2(1+1)(5(1)+4) = 9 RHS = LHS
Assume True: S(k) = 2+7+12+...+(5k+2) = 1/2(k+1)(5k+4)
Want to Show True: S(k+1) = 2+7+12+...+(5(k+1)+2) = 1/2((k+1)+1)(5(k+1)+4)
Here's what I have so far.
LHS = 2+7+12+...+ (5k+2) + (5(k+1)+2) = 5(k+1)+ 2 + 1/2(k+1)(5k+4) by induction hypothesis
I am stuck here...if anyone can help I appreciate it.
This is actually a sum of n+1 terms,Originally Posted by forumlurker
so you should have 2+7=0.5(2)9, for n=1,
in other words
You just need to continue on from where you were...
You are trying to prove if?
as you are using the "fact" that the sum of (n+1) terms should be
Here's one way to show it....
true
Yes I am trying to show that these are equal.
I understand till this point though.
My teacher has advised us to basically expandto
to prove they are equal.
And to stop any assumptions, this is not a homework problem, this is for me to learn. Although my instructor is helpful, he speaks quickly and is sometimes hard to understand.
Hi forumlurker,
If you are trying to discover if both sides are equal,
it's irrelevant whether you prove RHS=LHS or LHS=RHS.
However, sometimes you run into a teacher that will stick to one way.
The first term of this sum is (k+1) times the second term,
so we can write it as
proven
The induction process is not very complex here,
maybe it's the rearrangements of the factors you may not be used to.
I will gladly help you understand it completely,
tomorrow (as it's 4.40am here now!).
Which line are you stuck on?
You don't have to do it that way, either.
You can simply multiply out all the terms of both sides and show they are equal!!
+2+\frac{1}{2}(k+1)(5k+4)=5k+7+\frac{1}{2}\l eft(5k^2+9k+4\right)=)
=\frac{1}{ 2}\left(5k^2+19k+18\right))
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