Consider the sequences:

…

Formally we define the sequences by:

for all

Summing the first members of gives the th *triangle* number.

Summing the first members of gives the th *quadratic* number.

So, let’s generalise this:

Let be the set of numbers that you get by summing the first members of ; formally, set . So is the set of triangle numbers, is the set of quadratic numbers, and so on. Let .

**Problems:**

(1) Is bounded? (Equivalently, is there a positive integer such that for all with we have ?).

(2) If the answer to (1) is negative, what is the value of

?