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The nth term of a sequence is given by the formula n^3 + 11n . Find the first four terms of the sequence given by this formula and the first term of the sequence which is bigger than one million. Prove that all terms of the sequence are divisible by 6.

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Consider numbers of the form un = 1! + 2! + 3! +...+n!. How many such numbers are perfect squares?

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Investigate sequences given by $a_n = \frac{1+a_{n-1}}{a_{n-2}}$ for different choices of the first two terms. Make a conjecture about the behaviour of these sequences. Can you prove your conjecture?

Double Trouble

Stage: 4 Challenge Level: Challenge Level:1

Watch the videos carefully.

For the first video, what happens to the area remaining as Charlie adds on each new fraction?

For the second video, what is the relationship between the new area added, and the total area?