Proof and sequences:

- N is a positive integer, prove that n^3 - n^2 is always even
- Prove that the product of three consecutive integers is always be a multiple of 6
- Prove that the square of any odd number is always 1 more than a multiple of 8
- A sequence has all its terms positive. As N tends to be infinite, the nth term of the sequence approaches 3.

a. give a possible formula for the nth term of an increasing sequence with the properties above.

b. Give a possible formula for the nth term of a decreasing sequence with the properties above.

#### Top Answer

For 1 , 2 and 3 it is shown elaborately that the those conditions satisfies. For 4.... View the full answer