sona gold

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John Lee

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Posts: 2545

posted 15 years ago

I will try my best:

The top layer side length is 1 ball, layer sum is 1 ball;

The second layer side length is 2, layer sum is 3;

..................

So: sum = 1 + 2 + ... + side length = 1/2 * ( length + 1) * length;

................

So the twelveth layer has 78 ;

So the grand total is:

1 + 3 + 6 + 10 + 15 + 21 + 28 + 36 + 45 + 55 + 66 + 78 = 364 !

Originally posted by sona nagee:

one side of the bottom layer of a triangular pyramid has 12 balls. How many are there in the whole pyramid?

I will try my best:

The top layer side length is 1 ball, layer sum is 1 ball;

The second layer side length is 2, layer sum is 3;

..................

So: sum = 1 + 2 + ... + side length = 1/2 * ( length + 1) * length;

................

So the twelveth layer has 78 ;

So the grand total is:

1 + 3 + 6 + 10 + 15 + 21 + 28 + 36 + 45 + 55 + 66 + 78 = 364 !

sona gold

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Posts: 234

Johnson Chong

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Posts: 210

Johnson Chong

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Posts: 210

posted 15 years ago

Don Liu

Calculus of probabilities???!!!

What is that?

I've heard of calculus and probabilities but I just don't think I'll be able to find calculus of probabilities as a mathematical topic.

But I must say what a word.

Calculus of probabilities???!!!

What is that?

I've heard of calculus and probabilities but I just don't think I'll be able to find calculus of probabilities as a mathematical topic.

But I must say what a word.

-Surfing the JavaRanch in a sunny garden with a cold drink and laptop can't be beat. by Frank Carver(sheriff)

Jim Yingst

Wanderer

Sheriff

Sheriff

Posts: 18671

posted 15 years ago

One of the definitions of calculus is "A system or method of calculation". So "calculus of probabilities" just means "calculation of probabilities". As it happens though, serious probability theory has

*lots*of integrals in it, so you definitely need a good grasp of [integral] calculus to understand it."I'm not back." - Bill Harding, *Twister*

It is sorta covered in the JavaRanch Style Guide. |