On the Sum of Differentiable Functions

  title={On the Sum of Differentiable Functions},
  author={H. T. Croft},
Ryll-Nardzewski has proposed the following problem ( New Scottish Book , no. 119). If f n (x) are continuous, differentiable* functions in a closed finite interval, do there always exist constants c n (no c n = 0) (depending on the ), such that converges and is also a continuous differentiable function?