Investigate how you can work out what day of the week your birthday will be on next year, and the year after...
Show that if three prime numbers, all greater than 3, form an
arithmetic progression then the common difference is divisible by
6. What if one of the terms is 3?
Let S1 = 1 , S2 = 2 + 3, S3 = 4 + 5 + 6 ,........ Calculate S17.
The picture illustrates the sum $1 + 2 + 3 + 4 = (4 \times5)/2$. 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. See the problem Picture Story .