Question

Thực hiện phép tính:

1/1-x + 1/1+x + 2/1+x^2 + 4/1+x^4 + 8/1+x^8 + 16/1+x^16

Answer 1

\(\dfrac{1}{1-x}\)+\(\dfrac{1}{1+x}\)+\(\dfrac{2}{1+x^2}\)+\(\dfrac{4}{1+x^4}\)+\(\dfrac{8}{1+x^8}\)+\(\dfrac{16}{1+x^{16}}\)

=

=\(\dfrac{4}{1-x^4}\)+\(\dfrac{4}{1+x^4}\)+\(\dfrac{8}{1+x^8}\)+\(\dfrac{16}{1+x^{16}}\)

=\(\dfrac{8}{1-x^8}\)+\(\dfrac{8}{1+x^8}\)+\(\dfrac{16}{1+x^{16}}\)

=\(\dfrac{16}{1-x^{16}}\)+\(\dfrac{16}{1+x^{16}}\)

=\(\dfrac{32}{1-x^{32}}\)