The DU Lounge
Related: Culture Forums, Support ForumsHopeHoops
(47,675 posts)Orrex
(63,224 posts)First saw that on DU2 a few years back.
csziggy
(34,137 posts)I never made it to advanced mathematics.
SwissTony
(2,560 posts)The infinite series (the last component) can be evaluated as
S = 1/2 + 1/(2^2) + 1/(2^3) + ...
where S is the label form the sum and "^" is the exponentiation operator (2^3 = 2 to the third power = 2*2*2 = 8)
A simpler way to write it avoiding algebraic notation is
S = 1/2 + 1/4 + 1/8 + 1/16 +...
If we temporarily ignore the first term (1/2), we can extract 1/2 from ALL the remaining terms
S = 1/2 *(1/2)*(1/2 + 1/4 + 1/8 + ...)
Now if you look closely, the last term in brackets is just what I called S, so the equation now reads
S = 1/2 + (1/2)*S
Subtract (1/2)S from both sides gives
(1/2) S = 1/2
i.e. S=1
The second term is more complex. It comes from something called de Moivre's theorem, one of the results of which is that
e^(pi*i) = -1
pi is the old familiar 3.14, ratio of circumference to diameter of a circle
e is a good friend of pi and pops up lots in maths. It's roughly equal to 2.718
So that's the value of the last two terms, -1 and +1 respectively.
***HERE***
So the expression evaluates to
T = 0.002 -1 +1 = 0.002
i.e. 2 tenths of one cent. Mr Munroe is justifiably peeved at receiving this bill.
Bake
(21,977 posts)WHAT NOW, BITCHES????
Bake
SCantiGOP
(13,873 posts)My oldest daughter got called in several years ago because she had made some pretty bad mistakes on her tax form. I went with her, and the agent was polite, efficient, and wrote off some charges because she could tell they were errors and not any kind of attempt to avoid paying. I was impressed enough I wrote a letter to her supervisor.