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

2. 12 + 42 + 72 + ... + (3n - 2)2 = (n (6n^2 – 3n – 1)/2


For the given statement Pn, write the statements P1, Pk, and P(k+1).
3. 2 + 4 + 6 + . . . + 2n = n(n+1)


I'm rather confused - thank you!

Answer 1

here's the answer to your question!

Explanation:

Work shown in the attachment,

Refer to the attachment!