Note that ....Consider the series for 1/1+x = 1+x^2+.....+x^n (1)
now use that to find the series for 1/1+x^2 (which is basically replace x with x^2
1/1+x^2 = 1+x^2+x^4+....+x^2n (2)
and now find a series with 2x/1+x^2
basically multiply (2) with 2x ....
no my question is how do i find the series for
ln(1+x^2) using those facts above me
i used equation (2)
1+x^2 = 1/(1+x^2+x^4+....+x^2n)
now i log both sides
ln(1+x^2) = ln(1/(1+x^2+x^4+....+x^2n)
which gives me
ln(1+x^2) = -ln(1+x^2+x^4+....+x^2n)
is this correct ??
or am i going no where with this proof ?