expand (x^2+2x)/(2x^2+1) in ascending powers of x up to and including the term in x^5. state the range of values of x for which this expansion is valid.
find, in the simplest form, the coefficient of x^2017 in this expansion
(x^2+2x)/(2x^2+1) = 2x + x^2 - 4x^3 - 2x^4 + 8x^5 + ...
The (4k+1)st term is 2^(2k-1) x^(4k-3)
since 2017 = 4*505-3, the 2017th term is 2^1009 x^2017