Investigate how you can work out what day of the week your birthday will be on next year, and the year after...
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.
Let S1 = 1 , S2 = 2 + 3, S3 = 4 + 5 + 6 ,........ Calculate S17.
First prove the common difference must be even and then that it
must be divisible by 3. Think about possible remainders when the
middle number is divided by 3. Consider two cases.