Learn the fundamentals of the popular programming language JavaScript so that you can explore the realm of web development.

1. prove by mathematical induction that: 1+2^n<=3^n for all n>=1.

2. give an example or prove that there are none.

a) a simple graph with degrees 1,2,2,3.

b) a simple graph with degrees 2,3,4,4,4.

c) a simple graph with degrees 1,1,2,4.

2. give an example or prove that there are none.

a) a simple graph with degrees 1,2,2,3.

b) a simple graph with degrees 2,3,4,4,4.

c) a simple graph with degrees 1,1,2,4.

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Suppose 1 + 2^k <= 3^k for an k >= 1

you may try multiplying both side with (1+2) and see what happens.

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