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Resources tagged with Factorials similar to Growing:

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Challenge level: Challenge Level:1 Challenge Level:2 Challenge Level:3

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Broad Topics > Numbers and the Number System > Factorials

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Growing

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Fac-finding

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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.

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Weekly Challenge 36: Seriesly

Stage: 5 Short Challenge Level: Challenge Level:1

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

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Factorial

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

How many zeros are there at the end of the number which is the product of first hundred positive integers?

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Seriesly

Stage: 5 Challenge Level: Challenge Level:1

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

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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.

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N000ughty Thoughts

Stage: 4 Challenge Level: Challenge Level:1

Factorial one hundred (written 100!) has 24 noughts when written in full and that 1000! has 249 noughts? Convince yourself that the above is true. Perhaps your methodology will help you find the. . . .

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Factorial Fun

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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How Does Your Function Grow?

Stage: 5 Challenge Level: Challenge Level:1

Compares the size of functions f(n) for large values of n.