# Question: prove each of the statements using mathematical induction everything except...

###### Question details

Prove each of the statements using Mathematical Induction

everything except number 17

—6*7^N‐2*3^N is divisible by 4, for N>=1

--For any positive integer number n, n3+ 2 n is divisible by 3

---1+3+5+(2n–1)=n2

--Prove that n! > 2n for n a positive integer greater than or equal to 4.

--A 2n x 2n L‐shape, n >= 0, is a figure of the following form with no missing squares.

Use mathematical induction to prove that a 2n x 2n L‐shape can be tiled with trominoes (i.e. a 2 x 2 L‐shape)

--Provethat Tn =2n –1 forall n>=1 incaseitisknownthat T1 =1 and Tn =2Tn‐1+1.