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## Homework Statement

E

_{1}= {p

_{n}(t) = nt(1-t)

^{n}:n in N};

E

_{2}= {p

_{n}(t) = t + (1/2)t

^{2}+...+(1/n)t

^{n}: n in N};

where N is set of natural numbers

is the polynomial bounded w.r.t the supremum norm on P[0,1]?

## Homework Equations

supremum norm = ||*|| = sup{|p

_{n}(t)|: t in [0,1]}

## The Attempt at a Solution

I know that the set is bounded on P[0,1] if I can show that the supremum norm is less than some constant for all n. Can someone give me some advice on how to show either polynomial is bounded or not?

I think E

_{1}is unbounded, no matter your choice of t, since the polynomial's value will forever increase as n in increases. I feel the same can be said of E

_{2}but I know this is wrong.