Question

use binomial theorem to compute the square root of 17

Answer 1

\[(1+x)^{a}=1+ax+a(a-1)\,\frac{x^{2}}{2!}+a(a-1)(a-2)\,\frac{x^{3}}{3!}+...\]

\[(1+16)^{1/2}=1+\tfrac12(16)+\tfrac12(\tfrac12-1)\,\frac{(16)^{2}}{2!}+\tfrac12(\tfrac12-1)(\tfrac12-2)\,\frac{(16)^{3}}{3!}+...\]

Answer 2

thank you :)

Answer 3

@UnkleRhaukus did it cut off or was that the end of the problem ?

Answer 4

it's an infinite series, but i'm not sure if this is the right approach , because the series seams to diverge,

Answer 5

oh okay thank you