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!

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!

amistre64 · Answer

is it true for n=1?