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Resources tagged with Factorials similar to The Harmonic Triangle and Pascal's Triangle:

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Broad Topics > Numbers and the Number System > Factorials

The Harmonic Triangle and Pascal's Triangle

Stage: 5

The harmonic triangle is built from fractions with unit numerators using a rule very similar to Pascal's triangle.

Seriesly

Stage: 5 Challenge Level:

Prove that k.k! = (k+1)! - k! and sum the series 1.1! + 2.2! + 3.3! +...+n.n!

Weekly Challenge 36: Seriesly

Stage: 5 Short Challenge Level:

Prove that k.k! = (k+1)! - k! and sum the series 1.1! + 2.2! + 3.3! +...+n.n!

Fac-finding

Stage: 4 Challenge Level:

Lyndon chose this as one of his favourite problems. It is accessible but needs some careful analysis of what is included and what is not. A systematic approach is really helpful.

Growing

Stage: 5 Challenge Level:

Which is larger: (a) 1.000001^{1000000} or 2? (b) 100^{300} or 300! (i.e.factorial 300)

Factorial Fun

Stage: 5 Challenge Level:

How many divisors does factorial n (n!) have?

N000ughty Thoughts

Stage: 4 Challenge Level:

How many noughts are at the end of these giant numbers?