Recursive Summation indices stuck?

So I had to write a summation of S(n)=1 + 2^p + 3^p +...+ n^p

using recursive algorithms.

So far I have managed to do it without the 'p'

function y = SumR(n)
  y = n ;
  if n == 0
    y = 0 ;
  else
    y = y + SumR(n-1);
  end
  
end

yet obviously this doesn't give the answer, so I tried this instead but it doesnt seem to work annoyingly,

function y = S(n,p)
   y = n ;
  if n == 0
     y = 0 ;
           p = 0;
  else
    y = y + (S(n-1))^p;
  end
  
end

yet obviously its apparently not that simple, any help would be great thanks

Answer 1

[Walter Roberson]

y = y^p + S(n-1, p)