perplexus.info :: Sequences : Cross Product Equality Settlement

Cross Product Equality Settlement (Posted on 2010-10-04)

A sequence {x_n} is defined as:
x₁ = 2, and:
n*x_n = 2(2n-1)*x_n-1, whenever n ≥ 2

Prove that x_n is always an integer for every positive integer value of n.

Submitted by K Sengupta

Rating: 3.5000 (2 votes)

Solution: (Hide)

Refer to the solution submitted by broll in this location.

The sequence x(n) goes 2, 6, 20, 70, 252, 924, 3432 The OEIS A000984 gives the formula x(n) = (2n)! / (n!)^2, which Jer has proven in this location.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Full solution	Jer	2010-10-04 15:01:41
Possible Solution	broll	2010-10-04 13:35:44

Please log in:

Login:
Password:
Remember me:

Sign up! \| Forgot password

Search:

Search body:

Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (5)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:


perplexus dot info