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.
Show that if three prime numbers, all greater than 3, form an arithmetic progression then the common difference of the progression is divisible by 6. Find some examples of three primes which include the number 3 and form an AP, and show that in every such case the common difference is not divisible by 6.