Question

find the first 9th term of power series of sin x

Answer 1

derviables :)

Answer 2

\[ \sin(x) = \sum^\infty_{k=0} (-1)^k\frac{x^{2k+1}}{(2k+1)!} \]
You should be able to write out the first 9 terms.

Answer 3

x-x^3/6+x^5/120-x^7/5040+x^9/362880+O(x^10)

Answer 4

But thats only 5 terms..

Answer 5

\[ \sin(x)=x-{\frac {1}{6}}{x}^{3}+{\frac {1}{120}}{x}^{5}-{\frac {1}{5040}}{x}^
{7}+{\frac {1}{362880}}{x}^{9}-{\frac {1}{39916800}}{x}^{11}+{\frac {1
}{6227020800}}{x}^{13}-{\frac {1}{1307674368000}}{x}^{15}+{\frac {1}{
355687428096000}}{x}^{17}+O \left( {x}^{19} \right) )\]