tomorrow there will be an other lottery where the probability of winning is 1 in 2,000,000,000,000

the next day 1 in 3,000,000,000,000

the next day 4,000,000,000,000

after 100 days 100,000,000,000,000

the probability of winning the lottery is 1 in 1,000,000,000,000N

N = The number of days that has passed since day 1

etc

everyday the probabilities of winning the lottery are less.

John will buy 1 ticket every single day and he will play the lottery every single day for an infinite amount of time, will he ever win the lottery?

I´ll say that the answer is NO, but before justifying my answer I would like to read some opinions,