A calculus problem by Guilherme Dela Corte

Calculus Level pending

Evaluate, to three decimal digits, the value of $\alpha_{S}$ .

$\alpha_{S} = 1 + \sum_{m>0}\left ( \displaystyle \sum_{n\geq0} \dfrac{m^n}{n!} \right )^{-1}$

1 solution

Tanishq Varshney
Mar 22, 2015

$\displaystyle \sum_{m \geq 0}^{\infty}(e^{-m})$

= $\frac{e}{e-1}=1.5819$

Could you explain your procedures to us?

Guilherme Dela Corte - 6 years, 2 months ago

its a series expansion of $e^x$ $e^x=1+x+\frac{x^2}{2!}+\frac{x^3}{3!}+.............$

substitute $x=m$

Tanishq Varshney - 6 years, 2 months ago

You need to specify what happens when $m = n = 0$

Pi Han Goh - 6 years, 2 months ago

The question has been slightly altered. Thanks for the tip!

Guilherme Dela Corte - 6 years, 2 months ago