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c) STARTED FROM THE BOTTOM NOW WE HERE. STARTED FROM THE BOTTOM NOW MY WHOLE TEAM HERE.
Xn = Xn-1 + (1 + n)
X0 = 3
X1 = 3 + (1 + 1) = 5
X2 = 5 + (1 + 2) = 8
X3 = 8 + (1 + 3) = 12
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4a. Prove that if x is a rational number and x ≠ 0 then 1/x is a rational number
If x is a rational number ≠ 0, then it can be written as a/b, where a and b are integers and ≠ 0. Then 1/x is equal to 1/(a/b) which equals b/a. Therefore if x is a rational number, 1/x is also rational.
4b. Prove that if x is an irrational number and x≠ 0 then 1/x is an irrational number.
Assume that x is irrational and 1/x is rational. Then 1/x can be written as a/b where a and b are integers ≠ 0. So x is equal to 1/(a/b) which equals b/a, b and a are integers. Therefore x is rational. This contradicts the assumption that x is irrational. Therefore it is true that if x is irrational, 1/x is also irrational.
My name is Kenny Pang and my major is Applied Math. I got interested in math because I find it quite easy. I always get high grades in math classes without having to study much. I currently don’t have any goals after graduation. Maybe I will find a job and work for a couple of years then I may decide to do something else. What I hope to get out of this course is the programming knowledge which may help me in the future. Some of my hobbies are playing video games and watching movies.