Question

Prove that

d/dx (Yx) = 1/h (Yx+h – Yx–h) –1/2h (Yx+2h – Yx–2h) +1/3h (Yx+3h – Yx–3h) – ......... ...

Answer 1

$\frac{y(x+h)-y(x-h)}{h}-\frac{y(x+2h)-y(x-2h)}{2h}+\frac{y(x+3h)-y(x-3h)}{3h}-...=$

$=2y'-y'+2y'/3-2y'/4+2y'/5-...=2y'(1-1/2+1/3-1/4+1/5)=$

$=2y'ln2=1.386y'$