Question

Is anyone good at mathematical induction? I'm so confused!

Answer 1

I know that the first step is to make n=1 in the equation, but I don't understand the "n=k+1" part. Do I just input "k+1" every time there's an "n" in the equation?

Answer 2

Proof by induction first attempts to prove that the formula is true for k = 1. The process assumes that the result is true for n = k. Then the (k+1 )th term is added. If the resulting expression is the same as the expression for the sum for k terms except that k is replaced by (K+1) then this constitutes the proof.

Answer 3

* true for n = 1

Answer 4

- because if iot is true for n = 1 then it must be true for n = 2 , 3 etc

Answer 5

So, the first step would give you 1+3+5+...+(1)=1

Answer 6

And then if n=k, you get:
1+3+5+...+(2k-1)=k^2

Answer 7

No the first step is what is the sum of n terms if n = 1?
1 = first term so sum of 1 term = 1
n^2 = 1^2 = 1 = sum of 1 term

so true for n = 1

Answer 8

yes that is the sum of k terms

Answer 9

now add the (k + 1)th term

Answer 10

what is the formula for (k+1)th term
kth term = 2k - 1 right?

Answer 11

Ok, is this looking right so far?
1+3+5+...(2k-1)+(k+1)=k^2+(k+1)

Answer 12

Because I add the (k+1)th term to each side?

Answer 13

no the (k+1)th term is
(2(k + 1) - 1)