If your employer asked you to select one of these options:
option 1: your salary for the next two months will be $5,000.
option 2: 1 penny for the first day; then, he will double your salary every day for the next two months.
which would you pick and how much will your salary be at the end of the first month?

It would depend on the number of days in the month but the sequence is a geometric one.  And it grows very rapidly so I'd pick that, and the sum can be expressed as:

s(n)=a(1-r^n)/(1-r)  here a=0.01 (a cent) and r=2 so

s(n)=0.01(1-2^n)/(1-2)

s(n)=-0.01(1-2^n)  so just assume a 28 day month, in the first month you will earn

s(28)=-0.01(1-2^28)=$2,684,354.55  Yes that is over two and a half million dollars in the first month :P

On that 28th day you will earn:

a(28)=0.01(2^(28-1))=$1,342,177.28

Idon’t know actually is more difficult