Question 36
a) Find the value of the sum
$$
\frac{1}{1+1/x}+\frac{1}{1+x}
$$
b) Find the value of the sum
$$
\frac{1}{2019^{-2019}+1}+\ldots+\frac{1}{2019^{-1}+1}+\frac{1}{2019^{0}+1}+\frac{1}{2019^{1}+1}+\ldots+\frac{1}{2019^{2019}+1}
$$
$$
\frac{1}{1+1/x}+\frac{1}{1+x}
$$
b) Find the value of the sum
$$
\frac{1}{2019^{-2019}+1}+\ldots+\frac{1}{2019^{-1}+1}+\frac{1}{2019^{0}+1}+\frac{1}{2019^{1}+1}+\ldots+\frac{1}{2019^{2019}+1}
$$