powerful-thinking31.   Imagine the first number \(3^4\times 4^5\times 5^6\) is written out in full. How many zeros would there be at the end? Why? Can you find the answer without doing the whole calculation?

2.   Work out a few values of the second number \(1^n+2^n+3^n\) with n = 1, 2, 3 and 4 . Can you show numbers like this will be even for all values of n?

For what values of n will \(1^n+2^n+3^n+4^n\) be even.

What about \(1^n+2^n+3^n+4^n + 5^n\)?

What can you say about the sums of powers of the counting numbers 1, 2, 3, 4, 5, 6, 7, …p?

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