No, your argument is invalid, because you must realize that infinite summation is not commutative or associative, so putting brackets around certain numbers, and then re-ordering those numbers to change the order of the sum is not a valid operation.

## Not a valid operation

No, your argument is invalid, because you must realize that infinite summation is not commutative or associative, so putting brackets around certain numbers, and then re-ordering those numbers to change the order of the sum is not a valid operation.