Calculus Solution Manual Stewart

calculus solution manual stewart
Please help with Binomial series expansion!?

Use the binomial series to expand the function as a power series. State the radius of convergence. 1/(2+x)^3 …. I HONESTLY TRIED TO UNDERSTAND THIS BINOMIAL expansion CRAP except JAMES STEWARTS calculus book SUCK NUTSSSSS, SOOOO BADDD, and even the solutions manual as well, WOW CANT WAIT TO BURNNNNN THIS BOOK….
adude… WTF did you write dude…. woww.

http://en.wikipedia.org/wiki/Binomial_series

1/(2+x)³ = 1/[2(1+x/2)]³=(1/2³)*(1+x/2)⁻³ =

(1/2³)*{1+[(-3)/1!]*(x/2)+
[(-3)*(-4)/2!]*(x/2)²+
[(-3)*(-4)*(-5)/3!]*(x/2)³+
[(-3)*(-4)*(-5)*(-6)/4!]*(x/2)⁴+… } =

1/2³ -3x/2⁴+3*4x²/(2⁵2!) -3*4*5x³/(2⁶3!)+3*4*5*6x⁴/(2⁷4!) – … =

1*2/2⁴ -2*3x/2⁵+3*4x²/2⁶ -4*5x³/2⁷+5*6x⁴/2⁸ – … =

∑[n=0 to ∞] [(-1)ⁿ(n+1)(n+2)/2ⁿ⁺⁴]*xⁿ

The radius of convergence is finding by solving the inequality
|x/2|<1 ==> |x|<2 ==> R=2

Stewart Calculus 12_2_44