Geometry inmo problem

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0 replies

jlacosta

May 1, 2025

0 replies

Hard limits

Snoop76 6

N 2 minutes ago by Snoop76

$a_n$ and $b_n$ satisfies the following recursion formulas: $a_{0}=1,$ $b_{0}=1$ , $a_{n+1}=a_{n}+b_{n}$ $\text{[math]}$ and $\text{[math]}$ $b_{n+1}=(2n+3)b_{n}+a_{n}$ . Find $\lim_{n \to \infty} \frac{a_n}{(2n-1)!!}$ $\text{[math]}$ and $\text{[math]}$ $\lim_{n \to \infty} \frac{b_n}{(2n+1)!!}.$

6 replies

Snoop76

Mar 25, 2025

Snoop76

2 minutes ago

Real numbers

Jackson0423 0

6 minutes ago

Among any $n$ distinct real numbers, there exist two numbers $a$ and $b$ such that
$a^2 + b^2 < \sqrt{3}(1 + a^2b^2).$ Find the smallest possible value of $n$ .

0 replies

Jackson0423

6 minutes ago

0 replies

Sequences problem

BBNoDollar 1

N 12 minutes ago by BBNoDollar

Source: Mathematical Gazette Contest

Determine the general term of the sequence of non-zero natural numbers (a_n)n≥1, with the property that gcd(a_m, a_n, a_p) = gcd(m^2 ,n^2 ,p^2), for any distinct non-zero natural numbers m, n, p.

⁡Note that gcd(a,b,c) denotes the greatest common divisor of the natural numbers a,b,c .

1 reply

BBNoDollar

Yesterday at 5:53 PM

BBNoDollar

12 minutes ago

Prove XBY equal to angle C

nataliaonline75 1

N 32 minutes ago by cj13609517288

Let $M$ be the midpoint of $BC$ on triangle $ABC$ . Point $X$ lies on segment $AC$ such that $AX=BX$ and $Y$ on line $AM$ such that $XY//AB$ . Prove that $\angle XBY = \angle ACB$ .

1 reply

nataliaonline75

an hour ago

cj13609517288

32 minutes ago

No more topics!

Geometry inmo problem

Enes040612 2

N Apr 25, 2025 by Red_gear5246

Source: INMO 2008

Can anyone help with this problem? the book also starts the solution by saying IA1=IB1=IC1=2r which I'm not understanding why. The problem is at the attachments.

2 replies

Enes040612

Feb 13, 2025

Red_gear5246

Apr 25, 2025

Geometry inmo problem

G H J

Reveal topic tags

geometry

G H BBookmark kLocked kLocked NReply

Source: INMO 2008

The post below has been deleted. Click to close.

This post has been deleted. Click here to see post.

Enes040612

4 posts

Enes040612

#1 h Feb 13, 2025, 8:10 AM

Y by

Can anyone help with this problem? the book also starts the solution by saying IA1=IB1=IC1=2r which I'm not understanding why. The problem is at the attachments.

Attachments: