Hello,

An = e^(- 2√n)

the sequence converges, in that, as n increases, An approaches zero:

lim [e^(- 2√n)] =

n→∞

lim {e^[- 2√(→∞)]} =

n→∞

lim {e^[- 2(→∞)]} =

n→∞

lim [e^(→ - ∞)] =

n→∞

0

if the sequence actually is An = e^(- 2/√n), it likewise converges in that as n increases the exponent approaches zero and therefore An approaches 1:

lim [e^(- 2 /√n)] =

n→∞

lim {e^[- 2 /√(→∞)]} =

n→∞

lim {e^[- 2 /(→∞)]} =

n→∞

lim [e^(→0)] =

n→∞

e⁰ =

1

I hope it helps