Question

Use mathematical induction to prove the statement is true for all positive integers n, or show why it is false.

1. 4 ⋅ 6 + 5 ⋅ 7 + 6 ⋅ 8 + ... + 4n( 4n + 2) =( 4(4n + 1)(8n + 7)) / 6

I've only gotten this far: [4⋅6 + 5 * 7 + 6 * 8 + ... + 4n(4n + 2)] + 4(n + 1)(8n + 7)

2. 2. 1^2 + 4^2 + 7^2 + ... + (3n – 2)^2 = (n(6n^2 - 3n - 1)) / 2

3. For the given statement Pn, write the statements P1, Pk, and Pk+1.
2 + 4 + 6 + . . . + 2n = n(n+1)
I have no idea how to properly do these problems. Please show me the whole process of solving these problems, and the answers please! Thanks!

Answer 1

is it true for n=1?