There are many analogies between sums and integrals. And just as it is possible to have indefinite integrals, so indefinite sums can be set up by using symbolic variables as upper limits.
can do essentially all sums that are found in books of tables. Just as with indefinite integrals, indefinite sums of expressions involving simple functions tend to give answers that involve more complicated functions. Definite sums, like definite integrals, often, however, come out in terms of simpler functions.