Current source and resistor

An open circuit, by definition, can have no current. A current source, by definition, has a non-zero current. The two are in series so the currents must be equal, but can't be. You have created an impossible circuit.

The dual of your impossible circuit would be an ideal voltage source into a short:

^{simulate this circuit – Schematic created using CircuitLab}

A short, by definition, can have no voltage across it. A voltage source, by definition, does. The two are in parallel so the voltages must be equal, but can't be. This circuit is equally impossible.

You could say that the current in this circuit is infinite, and the the voltage in your circuit is infinite. What's the power in those circuits?

$$ P = I E = 1A \cdot \infty V = \infty W$$

$$ P = IE = \infty A \cdot 1V = \infty W $$

The power is infinite. What does that even mean? I have no idea: you will have to ask a mathematician.

If you were to consider that any two separated conductors are a capacitor, then maybe the circuit you had in mind was this:

^{simulate this circuit}

Then yes, the voltage across C1 will increase, linearly, forever.

Since someone else has provided an answer, I shall provide a more intuitive approach.

Since the two current sources are in parallel, combine the 2A and 1A sources into one 3A source and then you have the canonical current divider circuit.

^{simulate this circuit – Schematic created using CircuitLab}

$$I_{R1} = 3A \dfrac{R_2}{R_1 + R_2} = 3A \dfrac{6}{3 + 6} = 2A $$

etc.