12 + 42 + 72 + ... + (3n - 2) 2 = quantity n times quantity six n squared minus three n minus one all divided by two

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Mathematics

5 October, 21:27

12 + 42 + 72 + ... + (3n - 2) 2 = quantity n times quantity six n squared minus three n minus one all divided by two

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Dragster · Answer 1

The statement is false.

Proof by contradiction: Choose n = 1.

Then, 12 = 12.

Then, n (6n^2-3n-1) / 2 = 1 (6*1^2-3*1-1) / 2

= (6-3-1) / 2

= 2/2

= 1.

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

12 = 1.

This is a contradiction.

Therefore, the statement is false.