Question

Let bxc denote the greatest integer less than or equal to x. For example, b3:1c = 3
and b1:4c = 2.
Suppose that f(n) = 2n

1 +
p
8n 7
2

and g(n) = 2n +

1 +
p
8n 7
2

for each
positive integer n.
(a) Determine the value of g(2011).
(b) Determine a value of n for which f(n) = 100.
(c) Suppose that A = ff(1); f(2); f(3); : : :g and B = fg(1); g(2); g(3); : : :g; that is,
A is the range of f and B is the range of g. Prove that every positive integer m
is an element of exactly one of A or B

Answer 1

ah i cannot write it out properly nvm

Answer 2

? where is the b, c in greatest integer less than or equal to x? usually written as
\[[x]\]

Answer 3

see this

Answer 4

i need joemath's help

Answer 5

an interesting problem indeed! are we working on a b and c or just one of them?

Answer 6

umm i would like to be able to prove it too :D

Answer 7

it's a contest problem