Question

Is sais use induction to prove each conjecture is true for all positive n integers. what do I do?

Answer 1

`(6n+2)=n(3n+5)`

To prove if it is true for positive n intergers for induction method:

1. Prove For n=1

`\begin{gathered} (6(1)+2)=1(3(1)+5) \\ 6+2=3+5 \\ 8=8 \end{gathered}`

For n=1 it is true

2. Assume that the statement is true for n=k.

It is true for n=k

3. Prove For n=k+1

`\begin{gathered} (6(k+1)+2)=(k+1)(3(k+1)+5) \\ 6k+6+2=(k+1)(3k+3+5) \\ 6k+8=(k+1)(3k+8) \\ 6k+8=3k^2+8k+3k+8 \\ 6k+8=3k^2+11k+8 \\ 6k+8\\e3k^2+11k+8 \\ \end{gathered}`

As the conjeture is not true for n=k+1

The conjeture is not true for all positive intergers