Question

t1/2 means that the voltage (or charge) of the system will increase to half more of what is left in a time equal to t1/2 seconds. Therefore if a system is already at half charge (t1/2 seconds after starting) then after t1/2 more seconds the system will be charged to 50% plus half of 50%. That is 25% more, or 75% of the entire charge. Let's say that four t1/2's have gone by. That means that the charge (or voltage) is at (50% + 1/2*50% + 1/2*1/2*50% + 1/2*1/2*1/2*50%) = 93.75% of maximum charge. Yikes! Now look in your manual for a more simple mathematical derivation of this concept.

Answer 1

Fraction =∑
`t_(1/2)` / 2ⁿ n = 0, 1, 2, 3 ...

Step-by-step explanation:

Let's write this expression

Fraction = 50 + ½ 50 + ½ ½ 50 + ½ ½ ½ 50

Let's call the number as a

Fraction = a / 2⁰+ a / 2¹ + a / 2² + a / 2³

We can see that exponent is n = 0, 1, 2 ...

It can be written in summary form

Fraction = ∑ a / 2ⁿ

n = 0, 1, 2, 3

Fraction =∑
`t_(1/2)` / 2ⁿ n = 0, 1, 2, 3 ...

Where n is the number of cycles of
`t_(1/2)`