Question

Draw Pascal’s triangle up to and including the 5th row (n = 5).

Answer 1

Answer:

Looking at the first few lines of the triangle you will see that they are powers of 11 ie the 3rd line (121) can be expressed as 11 to the power of 2. This works till the 5th line which is 11 to the power of 4 (14641).An equation to determine what the nth line of Pascal's triangle could therefore be n = 11 to the power of n-1This works till you get to the 6th line. Using the above formula you would get 161051. The 6th line of the triangle is 1 5 10 10 5 1. Both numbers are the same. By inspection you will see that 161051 expressed in base 11 is in fact 1 5 10 10 5 1.The equation could therefore be refined as:n (base 11) = 11 to the power of n-1