Question

Prove that the sequence {an} defined by the relation
a1 = 1, an = 1 +1/1! +1/2! + ... +1/(n − 1)!
converges.

Answer 1

Is this a Quiz or a test?

Answer 2

its a question on my assigment

Answer 3

So what do you know so fat about this lesson?

Answer 4

what just happened?

Answer 5

bounded below...?

Answer 6

So what do you know so far about this lesson Mel?

Answer 7

idk

Answer 8

you have to work with me so i can help so please tell me what u understand and don't

Answer 9

i dont undersand the whole chapter

Answer 10

use the questions one

Answer 11

what does it mean to be bounded above or below
?

Answer 12

ok thank u

Answer 13

\[\frac{ a_{n} }{ a_{n-1} }=\frac{ \frac{ 1 }{ (n-1)! } }{\frac{ 1 }{ (n-2)! } }=\frac{ (n-2)! }{ (n-1)! }\]
\[=\frac{ (n-2) }{ (n-1)(n-2)! }=\frac{ 1 }{ n-1 }<1\]
so it is a decreasing function.
also \[\lim_{n \rightarrow \infty}\frac{ 1 }{ n-1 }\rightarrow 0\]
so it is convergent.