Prob. of >= 1 successes, exactly k successes in n trails?

[zorro]

Question : An infinite sequence of independent trails is to be performed . Each trail results in a success with the probability p and a failure 1-p . What is the probability that
i) at least 1 success occurs in the first n trails
ii) exactly k success occur in the first n trails
iii) all trails result in successes

Note : please provide only the end result ....Need to verify if its correct or no ?

[maggiemagnet]

please provide only the end result ....Need to verify if its correct or no ?

Please show your work and answer, so we can verify if your solutions are correct. Thank you!

[jk22]

Hi, nice to meet you.
did you get :
i) 1-(1-p)^n
ii) p^k(1-p)^(n-k)
iii)p^n->0 as n tends to infty ?

cya.