Three Sequences with Limit e
Three Sequences with Limit e
This Demonstration illustrates three convergent sequences with limit : =, =, and =1+1/1!+1/2!+..+1/n!. The first two converge slowly and the last one converges quickly. Use the second slider to choose so that if , then and are within of . Use the third slider to choose so that if , then is within of .
e
a
n
n
(1+1/n)
b
n
-n
(1-1/n)
c
n
m
n≥m
a
n
b
n
ϵ
e
k
n≥k
c
n
ϵ
e