Question

what if the calculation continued forever

Calculate:

1+(1/1)+(1/1x2)+(1/1x2x3)+(1/1x2x3x4)+... +...+...

Answer 1

@satellite73

Answer 2

no idea
is there a method you are supposed to use?

Answer 3

i believe its eulers formula

Answer 4

\[1+\frac{1}{1!}+\frac{1}{2!}+\frac{1}{3!}+...\] like that?

Answer 5

yes

Answer 6

oh , it is \(e\)

Answer 7

yes

Answer 8

if you replace \(1\) by \(x\) that is the expansion of \(e^x\)

Answer 9

could you please show it to me

Answer 10

\[e^x=\sum_{n=0}^{\infty}\frac{x^n}{n!}\]

Answer 11

so
\[e^1=\sum_{n=1}^{\infty}\frac{1}{n!}\]

Answer 12

is that the formula?

Answer 13

that is the power series expansion for \(e^x\) yes

Answer 14

sweet

Answer 15

that is a very very common and famous one
easy to remember too, so memorize it

Answer 16

so how can we find the answer?

Answer 17

i still dont know how to compute it

Answer 18

i mean how do you compute the part on your right hand side?