find-e-1-ln2-

Question Number 68068 by mhmd last updated on 04/Sep/19

f i n d e^{1 / l n 2} = ?

Commented by peter frank last updated on 04/Sep/19

e^{x} = 1 + x + \frac{x^{2}}{2!} + \frac{x^{3}}{3!} + \frac{x^{4}}{4!}

s u b s t i t u t e x = \frac{1}{l n 2}

Commented by mathmax by abdo last updated on 04/Sep/19

f o r x \neq 0 w e h a v e e^{\frac{1}{x}} = \sum_{n = 0}^{\infty} \frac{1}{n! x^{n}} = 1 + \frac{1}{x} + \frac{1}{2! x^{2}} + \frac{1}{3! x^{3}} + \dots

l e t t a k e x = l n (2) \Rightarrow e^{\frac{1}{l n 2}} = 1 + \frac{1}{l n (2)} + \frac{1}{2! {(l n 2)}^{2}} + \frac{1}{3! {(l n (2))}^{3}} + \dots

a n d i f w e w a n t a s p p r o x i m a t e v a l u e w e c a n t a k e 10 t e r m s

f o r t h i s s e r i e .