15 Jun '10 04:172 edits

Just a few problems I came up with, none of them too hard.

1). 1,2,5,14: find the next term and a formula for the nth term.

2). I have 7 dice, each of which I role 1 time per game. I have to pay $0.50 per game. If the total sum of all my dice is less than 10 or more that 39, I win the jackpot of $1,000,000. Is this game worth playing, assuming I have all the time in the world, will continue playing for ever? What is the expected gain/loss for every time I play?

3). Not really a problem, just something to think about: Is infinity + 1 greater than or equal to infinity?

1). 1,2,5,14: find the next term and a formula for the nth term.

2). I have 7 dice, each of which I role 1 time per game. I have to pay $0.50 per game. If the total sum of all my dice is less than 10 or more that 39, I win the jackpot of $1,000,000. Is this game worth playing, assuming I have all the time in the world, will continue playing for ever? What is the expected gain/loss for every time I play?

3). Not really a problem, just something to think about: Is infinity + 1 greater than or equal to infinity?