What is the series expansion of sin^-1(x) at x = 0. Please give 3-5 terms of the expansion with steps if possible.Thanks for your help.
Taylor Series around x = 0
x + x^3/6 + (3 x^5)/40 + (5 x^7)/112 + (35 x^9)/1152 + (63 x^11)/2816
Taylor series expansion can be used here as follows:
Series expansion at x = 0:
Sin^-1(x) =x + x^3/3! + 3^2.x^5/5! + 3^2.5^2.x^7/7! + 3^2.5^2.7^2.x^9/9! + 3^2.5^2.7^2.9^2.x^11/11!.......and so on.
This is the same as:
Sin^-1(x) = x + [1/2.3]x^3 + [1.3/2.4.5]x^5 + [1.3.5/184.108.40.206]x^7 + [220.127.116.11/18.104.22.168.9]x^9....etc.
The steps here are self-explanatory.