Calculator function

[kendor]

Here's one for you Mathmaticians out there, On my scientific calculator I have a Factorial key X! that multiplies all the number up to and including the one entered ie 3 X! = 6 (1x2x3) but what function if there is one that does the same but with addition instead of multiplication?
not too hard with small numbers to add them together but when it comes to large ones it would be quite a task.
Anyone out there got any solutions?

 

[TexMex]

You could always use the time honoured method of adding the first number in the sequence, to the last and then multiplying by half of the number of values in the series.

eg. to find the sum of all the numbers from 1 to 100
(1+100) * 50 = ie 5050

I've never seen the X! function key on a calculator. Sounds a bit extraneous. Do you use it often

 

[securespark]

Sounds a bit extraneous.

What, like conductive parts? OOPS!!

 

[pipme]

n terms.
a First term.
d Common difference.
Sum of arithmetic progression ( n / 2 ) ( 2a + ((n - 1) d ) )

eg.
5 numbers first number 6 common dif 2

6;8;10;12;14 sum = 50 By calc 5/2 ( 12 + (4(2))) .... 2.5 (12+8 ) ...
2.5x20=50 Bish, bash, bosh as they say !! Oh to be an engin-bludy-eer !!

the ! or factorial function can be used in working out combinations and permutations.

Geometrical progression is the one to know ... used in mortgage and loan calculations ...oooer !!

P

 

[TexMex]

( n / 2 ) ( 2a + ((n - 1) d ) )

since a+(n-1)d = last number;
and a = first number

(2a +((n-1)d) = first number + last number

Substituting in your original equation
(n/2)(first number + last number)

which is what I said.

so for the sequence you described. using my simplified method.
2.5 *(6+14) = 50

Surely that's simpler.

 

[securespark]

Read down Pip's list of bold letters - is he being rude?

N A D S............

 

[oilman]

Surely that's simpler

It is, but it works for only one case, whereas the method pipme described is a general solution.

Surely that's better?

 

[kendor]

Thanks for your help guys, I'm surprised there's not a key for it like the X! function.

 

[pipme]

Yep, just the general progression.

Like Any 3 from 6 = ?
6x5x4 / 3x2x1 cancels to 5x4 / 1 = 20 bets

any 4 from 8 .... 8x7x6x5 / 4x3x2x1 .... 1x7x6x5 / 1 = 70 bets

But the 'general' utilises ! factorial.

e.g. Any 8 from 12 requires ? bets

12! / ( 8! ( 12-8 )! )

Any 8 from 12 ... 12x11x10x9x8x7x6x5 / 8x7x6x5x4x3x2x1
reduces to 11x5x9 / 1 = 495 bets
By the general method using factorial !

479001600 / ( 40320 ( 24 ) ) .... 479001600 / 967680 = 495
Using a calculator with the ! factorial function becomes easy ... even easier with the nCr function.

Football pools, gambling etc
P

 

[pipme]

Wot a luvly summer !!