[Dylan16807]

Okay the reply got deleted but I already did all this math so I'm going to post anyway.

> [only able to use the cap from 4V to 3V]

> (C * 1V * 1V)/2

> [you'll need 1000mF]

Wrong equation. That's the energy from 0V to 1V. Each incremental volt stores more power than the last. 0V-3V is 9x that amount, and 0V-4V is 16x that amount, so 3V-4V is 7x that amount, and you'll need 140mF.

But also it shouldn't be connected directly in parallel to the battery; so I'd think of it more as 4.2V to 2V of supply. That would mean you need 74mF.

So put in two and you'll more than hit the target.

Even better, if you expect the battery to contribute some, you only need the one.