Use a calculator to evaluate the following expression:

48!/(48-2)!2!

Rewrite the following sum using summation notation. Represent the index and lower limit of the summation as k and any number of your choice, respectively. Do not evaluate.

(p + q) + (p + 3q) + (p + 5q) + ⋯ + [p + (2n - 1)q]

A factorial is used in the general term of a sequence, which is given. Write the sequence's first four terms. 

a_n = 3(2n-1)!

Write the first four terms of the sequence using the recursion formula. 

a₁ = 8 and a_n = 6a_n-1 + 1 for n≥2

Write S_k and S_{k + 1} for the given statement S_n where n is any positive integer. Simplify S_{k + 1} fully.

S_n: 2 is a factor of n² + 3n.