Real Analysis Answers

using principle of mathamatical induction prove that a+(a+d)+(a+2d)+...........+[a+(n-1)d] =
n/2[2a+(n-1)d]

Show that the closure of a set equals the union of the set and its complement.

Is their a connection between Dzeta function and prime numbers?
If there is, then show it, else explain why.

show that the union of finite set is finite

Find all real numbers x that satisfy the following inequalities.
1<x2<4

Find Laplace transform F(p) for function f(t)=erf(sqrt(t))

Find Laplace transform F(p) for function f(t)=ln(t)

Find Laplace transform F(p) for function S(t) - sin-Frenele integral

Find Laplace transform F(p) for function f(t)=(t^n)sh(at)/n!