Yes i am going to memorize it, it is quite simple if you know the first.
For the last one, note that you can simplify since the second part of the numerator is equal to a constant times the denominator, it can be writen as :
Tax_on_OrdinaryIncome + (1+r)^n/(Same denominator as for the other cases)
As explained by grad4, the new coefficient comes from the fact gift to charitable oranisation are tax deductible for the giver .
Let assume for simplicity re=rg=0 , Te=0 and the tax rate on ordinary income of the giver Tio is 40%;
The giver gives 100$ , but he receives 40$ back as a tax deduction (Tio*Amount give), that he will be able to give later. If he give those 40$ that he received as a tax deduction in his bequest, the charitable organisation will have receive 140
If he wait until his death, he will not be able to use the tax deduction and only gives 100$ at his death.
The ratio is 140/100 = (1+r)^n/(Same denominator as for the other cases) + Tax_on_OrdinaryIncome
= 1 + 0.4 with our assumption