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# Proof and sequences:

Proof and sequences:

1. N is a positive integer, prove that n^3 - n^2 is always even
2. Prove that the product of three consecutive integers is always be a multiple of 6
3. Prove that the square of any odd number is always 1 more than a multiple of 8
4. 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.

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

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