and 
Prove that
is the infinite sum 
.
since 
,
,
So is 
be a set of integers satisfying the following property: For every positive integer 
and every set of coefficients 
,
are also elements of 
where 
are positive integers. Prove that 
and 
verifying 
. 
Y by skyguy88, ChampionGirl, Mango247, Mango247
10. At Pizza by Alex, toppings are put on circular pizzas in a random way. Every topping is placed on a randomly chosen semicircular half of the pizza and each topping’s semi-circle is chosen independently. For each topping, Alex starts by drawing a diameter whose angle with the horizontal is selected uniformly at random. This divides the pizza into two semi-circles. One of the two halves is then chosen at random to be covered by the topping.
(a) For a 2-topping pizza, determine the probability that at least
of the pizza is covered by both toppings.
(b) For a 3-topping pizza, determine the probability that some region of the pizza with non-zero area is covered by all 3 toppings.
(c) Suppose that
is a positive integer. For an -topping pizza, determine the probability, in terms of , that some region of the pizza with non-zero area is covered by all toppings.
I already solved (a), but I don't seem to be able to do (b). Is there any trick to tackle this problem?
(a) For a 2-topping pizza, determine the probability that at least
of the pizza is covered by both toppings.(b) For a 3-topping pizza, determine the probability that some region of the pizza with non-zero area is covered by all 3 toppings.
(c) Suppose that
is a positive integer. For an -topping pizza, determine the probability, in terms of , that some region of the pizza with non-zero area is covered by all toppings.I already solved (a), but I don't seem to be able to do (b). Is there any trick to tackle this problem?
