How to define function with indexed variables and sum

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I would like to define a function f(n)=sum(x[k]*x[k+1], k= 1..n) so that it produces expressions like this:

f(1)= x[1]*x[2],
f(2)=x[1]*x[2]+x[2]*x[3]
f(3)=x[1]*x[2]+x[2]*x[3]+x[3]*x[4]

How to do this in sage? I tried to generate indexed variable with the following:

class VariableGenerator(object):
      def __init__(self, prefix):
          self.__prefix = prefix
      @cached_method
      def __getitem__(self, key):
          return SR.var("%s%s"%(self.__prefix,key))

x=VariableGenerator('x')
k, n = var('k,n')
f(n)=sum(x[k], k, 1, n)

Unfortunately this does not work. Any ideas?