# 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