Question

Find the sum of the series: 1+1+1/2!+1/3!+1/4!+1/5!+...= e.

So I'm thinking to use the equation sum= a/1-r , but I'm not sure what r is in this case?

Answer 1

Do you know the infinite series (or Taylor Series) of \[e^x\]?

Answer 2

you can use 1/1-r because it is not geometric series

Answer 3

* can't

Answer 4

x^n/n!

Answer 5

right!, you get:\[e^x=1+x+\frac{x^2}{2!}+\frac{x^3}{3!}+\cdots\]can you think of a clever value of x to plug in this equation that gives you your series?

Answer 6

1?

Answer 7

perfect :)

Answer 8

so youve shown that:\[e^1=1+1+\frac{1}{2!}+\frac{1}{3!}+\frac{1}{4!}+\cdots=e\]

Answer 9

Ooo, I see. Thank you! :)