Assignment:
By using partial fractions show that
a. The sumation from 0 to infinity of 1/(n+1)(n+2)=1
b. The sumation from 0 to infinity of 1/(α+n)(α+n+1)=1/α >0 if α>0
c. The sumation from 0 to infinity of 1/n(n+1)(n+2) =1/4
Apply the theorem: let (Xn) be a sequence of positive real numbers such that L := lim(Xn+1/ Xn) exsists. If L>0 then (Xn) converges and lim(Xn)=0
Apply this theorem where a,b satisfy 0 < a < 1, b > 1
a. (a^n)
b.(b^n/2^n)
c.(n/b^n)
d.(2^3n/3^2n)
Provide complete and step by step solution for the question and show calculations and use formulas.