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( 1 2 pts ) a ) ( 5 pts ) Use the Principle of Mathematical Induction to prove that 4 + 8 + 1

(12 pts)
a)(5 pts) Use the Principle of Mathematical Induction to prove that
4+8+12+16+cdots+4n=2n(n+1) for all n1. Show all the steps
b)(4 pts) Give a recursive definition with initial condition for the following function.
f(n)=(3n)!,n=0,1,2,dots
c)(3 pts) In a certain lottery game you choose a set of six numbers out of 30 numbers.
Find the probability that exactly one of your numbers match the six winning numbers.
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