# How to define function with indexed variables and sum

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?

Would defining

`f`

as a Python function work for you?`f = lambda n: sum( x[k] for k in range(1,n+1) )`