Correct use of bound/bounded

Solution 1:

Verb: bind
Past: bound
Noun: a binding (in some senses)
Used in various senses in physics and computer science but not in mathematics.

Verb: bound
Past: bounded
Noun: a bound
Used in mathematics and computing to denote a range or finite area in which a value must be.

The sentence in your question is about a bound, therefore the past participle is bounded.

All partial sums of two given sequences are bounded by a positive constant.
There is a bound on the partial sums of two given sequences.

Solution 2:

The difficulty you are facing is that there are two separate verbs in play here.

The verb bind means

Tie or fasten (something) tightly

Its past tense and past participle is bound

The verb bound (present tense) means

Form the boundary of; enclose

or

Place within certain limits; restrict

Bound can also mean

to move with a leap or series of leaps

In each of these cases, the past and past participle form of bound is bounded.

In the example given by the OP, it seems that the meaning is to place within limits (rather than to tie to). The verb would then be bound and the past participle is bounded. In the construction given, bounded is correct and bound is not.