Question

Show that the sequence 2

nx

nxe



  is point-wise convergent at the interval 0,k,

k>0but is not uniformly convergent at that interval.​

Answer 1

Answer:

The series ∑fn, whose sum to n terms, Sn(x). 2nx nxe−. = , is pointwise and not uniformly convergent on any interval [0, k], k > 0.