exponential

question is not clear, since you have not state the definition of t and n.

BTW, the proof of the first part is:

e = lim_(t->inf) (1+1/t)^t

lim_(t->inf) (1+x/t)^t
= lim_(t/x->inf) ((1+x/t)^t/x )x

let y=t/x
= lim_(y->inf) ((1+1/y)^y )x
= e^x