Reference no: EM132323105

Assignment - Solve the problems and write the solution in LaTeX:

1. For every integer n ∈ N, it follows that 1² + 2² + 3² + 4² + · · · + n² = (n(n+1)(2n+1))/6.

2. If n ∈ N, then 1·2 + 2·3 + 3·4 + 4.5+ · · · + n(n+1) = (n(n+1)(n+2))/3.

3. For every natural number n, it follows that _i=1∑ⁿ(8i - 5) = 4n² - n.

4. If n ∈ N, then 1/2! + 2/3! + 3/4! + · · · + n/(n+1)! = 1 - 1/(n+1)! .

5. For any integer n ≥ 0, it follows that 3|(5²ⁿ - 1).