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Natural Sum

The picture illustrates the sum 1 + 2 + 3 + 4 = (4 x 5)/2. Prove the general formula for the sum of the first n natural numbers and the formula for the sum of the cubes of the first n natural numbers.

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Series Sums

Let S1 = 1 , S2 = 2 + 3, S3 = 4 + 5 + 6 ,........ Calculate S17.

Prime AP

Stage: 4 Challenge Level: Challenge Level:1

Why do this problem?
A non standard problem on prime numbers and AP's that requires some careful mathematical reasoning

Possible approach
Let the class work at first individually and then is small groups. Discuss their findings. If they have not met modulus arithmetic, or the usual notation, then introduce this notation as a standardised way of recording the reasoning in this solution.

Key questions
How can we be sure we have considered all possible cases?