User Fawkes4494d3

14 votes

$\frac{1}{A_1A_2}=\frac{1}{A_1A_3}+\frac{1}{A_1A_4}$.Then find the value of $n$

answered Aug 9, 2015 at 8:09

13 votes

Prove that 10101...10101 is NOT a prime.

answered Feb 11, 2016 at 0:25

8 votes

Accepted

Shorter way to calculate number of ways to distribute varying number of balls into 3 distinct boxes such that sum of balls $\leq$ 99

answered Aug 28, 2020 at 7:21

8 votes

Prove that if x,y,z are positive integers such that $x^3+y^3+z^3=3(x+y+z+xyz)$ then they must be consecutive numbers

answered Oct 8, 2020 at 4:55

6 votes

Numbers from $1,\frac12,\frac13,...........\frac{1}{2010}$ are written and any two $x,y$ are taken and we replace $x,y$ by just $x+y+xy$

answered Aug 16, 2020 at 17:04

5 votes

Accepted

Calculate Probability of arrangements

answered Aug 27, 2020 at 16:24

5 votes

Accepted

Evaluating $\sum_{n=k}^{\infty} \frac{1}{ \binom{n}{k}}$

answered Sep 17, 2020 at 3:05

4 votes

Alternating Sequences of Length five

answered Sep 21, 2020 at 16:16

4 votes

$|_{x=1}$ notation?

answered Sep 8, 2020 at 9:25

3 votes

Maximize $\frac{xe^x}{e^x-1}$

answered Sep 1, 2020 at 23:33

3 votes

Can a critical point be a minima or maxima even if its $f ''(c)=0$?

answered Aug 30, 2020 at 8:11

3 votes

Accepted

Prove that if $YA\cdot YB=YX\cdot YM$ then $(A,B;X,Y)=-1$ .

answered Aug 16, 2020 at 15:26

3 votes

Semicircle Question

answered Aug 28, 2020 at 10:31

3 votes

Accepted

Find the length of $DE$

answered Aug 30, 2020 at 5:54

3 votes

Accepted

Median of triangle and tangents

answered Aug 24, 2020 at 3:03

3 votes

How to calculate the length $AH$?

answered Jul 13, 2020 at 9:39

2 votes

how to prove the binomial equation below

answered Jul 1, 2020 at 11:23

2 votes

How to compute a simple sum

answered Jul 2, 2020 at 0:45

2 votes

In an isosceles triangle with base $AB$ and $\angle CAB=80^\circ$ taken $D$ on $CA$, $E$ on $CB$ such that ...

answered Jun 30, 2020 at 1:04

2 votes

How to solve in terms of k the following equation?

answered Jun 22, 2020 at 11:06

2 votes

Accepted

Show that $A^2=A$ suppose that A is normal and $A^5=A^4$

answered Aug 14, 2020 at 16:30

2 votes

Sum coefficients

answered Jul 30, 2020 at 17:33

2 votes

Accepted

Question about convexity: how do we prove that $\displaystyle \sum_{i=1}^{k}p_{i}b_{i}\geq\prod_{i=1}^{k}b^{p_{i}}_{i}$?

answered Aug 6, 2020 at 22:22

2 votes

How to prove that $f: \mathbb{R} \to \mathbb{R}$ is continuous, given that $xy-y^2 \leq f(x)-f(y) \leq x^2-xy$?

answered Aug 30, 2020 at 7:41

2 votes

Is it possible to solve this identity by "inspection"?

answered Aug 29, 2020 at 22:19

2 votes

Accepted

Pdf of $Y = X^2$ when $X$ has pdf $f(x) = 2x$ for $0 < x < 1$

answered Aug 29, 2020 at 16:52

2 votes

Was I on the right track with this circle-tangent geometry problem solution? How are you supposed to solve it?

answered Aug 28, 2020 at 2:43

2 votes

Accepted

Prove the relation $\mathsf{H}(AB,CH)$

answered Sep 22, 2020 at 16:59

2 votes

Accepted

RMO 1991 question 4

answered Sep 1, 2020 at 21:48

2 votes

Accepted

Two diagonals of a regular heptagon are chosen. What is the probability that they intersect inside the heptagon?

answered Sep 10, 2020 at 23:45

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116 Answers

$\frac{1}{A_1A_2}=\frac{1}{A_1A_3}+\frac{1}{A_1A_4}$.Then find the value of $n$

Prove that 10101...10101 is NOT a prime.

Shorter way to calculate number of ways to distribute varying number of balls into 3 distinct boxes such that sum of balls $\leq$ 99

Prove that if x,y,z are positive integers such that $x^3+y^3+z^3=3(x+y+z+xyz)$ then they must be consecutive numbers

Numbers from $1,\frac12,\frac13,...........\frac{1}{2010}$ are written and any two $x,y$ are taken and we replace $x,y$ by just $x+y+xy$

Calculate Probability of arrangements

Evaluating $\sum_{n=k}^{\infty} \frac{1}{ \binom{n}{k}}$

Alternating Sequences of Length five

$|_{x=1}$ notation?

Maximize $\frac{xe^x}{e^x-1}$

Can a critical point be a minima or maxima even if its $f ''(c)=0$?

Prove that if $YA\cdot YB=YX\cdot YM$ then $(A,B;X,Y)=-1$ .

Semicircle Question

Find the length of $DE$

Median of triangle and tangents

How to calculate the length $AH$?

how to prove the binomial equation below

How to compute a simple sum

In an isosceles triangle with base $AB$ and $\angle CAB=80^\circ$ taken $D$ on $CA$, $E$ on $CB$ such that ...

How to solve in terms of k the following equation?

Show that $A^2=A$ suppose that A is normal and $A^5=A^4$

Sum coefficients

Question about convexity: how do we prove that $\displaystyle \sum_{i=1}^{k}p_{i}b_{i}\geq\prod_{i=1}^{k}b^{p_{i}}_{i}$?

How to prove that $f: \mathbb{R} \to \mathbb{R}$ is continuous, given that $xy-y^2 \leq f(x)-f(y) \leq x^2-xy$?

Is it possible to solve this identity by "inspection"?

Pdf of $Y = X^2$ when $X$ has pdf $f(x) = 2x$ for $0 < x < 1$

Was I on the right track with this circle-tangent geometry problem solution? How are you supposed to solve it?

Prove the relation $\mathsf{H}(AB,CH)$

RMO 1991 question 4

Two diagonals of a regular heptagon are chosen. What is the probability that they intersect inside the heptagon?