10 Answered Questions for the topic Math Proofs

02/25/18

#### Induction proofs

Exercise 2.25: P(n) is the number of regions in the plane formed by n lines in general position: n=1, p(n)=2; n=2, p(n)=4; n=3, p(n)=7; n=4, p(n)=11; n=5, p(n)=16; n=6, p(n)=22.2.76) Finish the...
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02/21/18

#### Prove that for any integer z that is a perfect square, there exists integers m and n such that m^2+n^2=zk.

Let k be an integer such that there exist integers p and q with p^2+q^2=k.
Prove that for any integer z that is a perfect square, there exists integers m and n such that m^2+n^2=zk.

11/07/17

#### The question is about proving limits

a) Show that if xn≠0, where n(∈) is a subset of N then lim(xn)=0 if and only if lim(1/xn2)=infinity
b) Give an example for which lim(xn)=0 but lim(1/x2n) does not exist

11/28/16

#### Given: line WXY, m<WXZ = 135°. Prove: m<ZXY = 45°

Statements
line WXY
m<WXY = 180°
m<WXZ = 135°
m<WXY = m<WXZ + m<ZXY
180° = 135° + m<ZXY
45° = m<ZXY
m<ZXY = 45°
Reasons
Given
Defintion of supplementary...
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10/15/16

#### Prove or disprove,n is a rational number, 1/n does not equal n-1

Prove or disprove,n is a rational number, 1/n ≠ n-1

03/21/16

#### prove that there does not exist n belongs to N such that n congruent 2 (mod 4) and n congruent 4 (mod 8)

prove that there does not exist n∈N such that n≡2 (mod 4) and n≡4 (mod 8). Please help this was on my last exam but I was very lost and my professor did not have enough time to go over it in class.

10/21/15

#### What is the minimum height height of a full binary tree?

What is the minimum height of a full binary tree T which has nodes n(T) = 2k-1 for k= 1, 2, ... ?

06/10/15

#### fn(x)=1/(x+1/(2n)) and fn(x)=1/(x+1/(n^2)).

Q1 prove piecewise convergent on (0,infinity)
Q2 prove uniform convergent on [1,infinity)
Please help with these two equations. Much Thanks, it's preparation for final exam

02/13/15

#### How to prove that there is no r in the rationals such that r^2 = 6

Can someone help me write a full proof for this

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