Sum of integers (tam sayıların toplamı)

[Haluk]

Herkese merhaba;

Forumun yeni bölümüne ilk soruyu ben yazayım ... :mrgreen:

Soru, 1' den başlayarak herhangibir sayıya kadar olan tam sayıların toplamını bulunması ile ilgili.

Diyelim ki, sayımız 1.000.000.000 olsun.

1 + 2 + 3 + 4 + 5 + .............. + 999.999.999 + 1.000.000.000 = ?


******************************************************

Hi all;

Let me be the first one, posting on this new part of the board ... :mrgreen:

The question is, finding the sum of the integer numbers starting from 1, to the number under concern.

So, let's assume the number is 1.000.000.000

1 + 2 + 3 + 4 + 5 + .............. + 999.999.999 + 1.000.000.000 = ?

 

[Recep İpek]

Sub Total()
Endnumber = InputBox("Entry Number End.", "Number", 1000)
If Not IsNumeric(Endnumber) Then Exit Sub
For i = 1 To Endnumber
Totalnumber = Totalnumber + i
Next i
MsgBox Totalnumber
End Sub

 

[Levent Menteşoğlu]

Simple solution by using Gauss method

1 + 2 + 3 + 4 + 5 + .............. + 999.999.999 + 1.000.000.000

1.000.000.000+999.999.999.....................+2+1

1.000.000.001 x 1.000.000.000/2=5E+17

 

[Ali]

If you want to use Excel standart function.Can you try this formula.

I assumed A500 cell (your last cell) . You must write this formula into B1 cell

=(A500*(A500+1))/2

 

[Haluk]

Hi ripek, leventm and fructose;

This is the problem ...

ripek's code seem to be correct and, leventm's Gauss theorem is also correct.

But the results are different... :mrgreen:

I've tried code similar to ripek's, and got the answer as :
500. 000. 000. 067. 109. 000

I also tried leventm's approach before, and got the result as :
500. 000. 000. 500. 000. 000

Also, I tried a similar routine in C language, but that code also yielded the same result in VBA.

So, this is the real question ..... why are they different ? .... :mrgreen:

I' ve some ideas but not sure ...

 

[Ali]

Hi Haluk;

Hi ripek, leventm and fructose;


So, this is the real question ..... why are they different ? .... :mrgreen:

I' ve some ideas but not sure ...

Are you sure :mrgreen:

Did you try to separate Levent's code parenthesis.

I think,We must to pay attetion procedure priority

I tried ripek's code and Levent's code.

The results same.

 

[Levent Menteşoğlu]

I have also tried Ripek's code, The results are not same, Haluk's right

 

[Ali]

I' ve some ideas but not sure ...

Would you share your opinion about this topic with us

I crousied this matter.

 

[Recep İpek]

.....I think......

 

[Merhum İdris SERDAR]

I am not sure. But may be the reason arises from digits' limit in excel.
Because, as far as I know the limit of digit in Excel is 16.

 

[Haluk]

I thought the same .... as yurttas and that's why I tried in C hoping to get a more reliable result.

But, this or that .... every program has some limits.

One of the things what I think is that; because Excel has some trouble in dealing with large numbers in a big for-next loop, I decided to divide the number (i.e. 1.000.000.000) in smaller parts and perform the calculation.

Something like this;

DefDbl A-Z
'
Sub Test()
    i = 1000000000 / 5
    For x = 1 To i
        y = y + x
        z = z + i * 1 + x
        z2 = z2 + i * 2 + x
        z3 = z3 + i * 3 + x
        z4 = z4 + i * 4 + x
    Next
    [A7] = (y + z + z2 + z3 + z4)
End Sub

The above procedure gives the result as :
500.000.000.111.503.000

As per my last coding stated above, when I performed the procedure by 4 subtotals instead of 5, I' ve got the result as :
500.000.000.098.792.000

So, what I see from here is that .... by increasing the amount of subtotals, we can achieve more reliable results.

Having said this ..... if we are not using Excel to program a spaceship landing to moon, we can use it safely in our daily routines... as long as we are not dealing with large numbers....... :mrgreen:

 

[Levent Menteşoğlu]

if we are not using Excel to program a spaceship landing to moon

this may be possible by version Excel 2100.

 

[Ivan F Moala]

this may be possible by version Excel 2100.

Yes, how true.
unfortunateley all software such as Exel that depend/use the IEEE
floating point standard will yield only up to 15 decimal places. Even with this
"accuracy", many numbers are represented as an approximation of their "true" value.

 

[mehmett]

Welcome to Excel.Web.Tr Mr Moala,

Nice to meet you.

 

[Recep İpek]

Welcome Mr Moala,

 

[Ivan F Moala]

Welcome to Excel.Web.Tr Mr Moala,

Nice to meet you.

Thankyou for the welcome mehmett.

It is nice to be here.


Tanıştığımıza memnun oldum.

 

[Ivan F Moala]

Welcome Mr Moala,

Merhaba! ripek, Tanıştığımıza memnun oldum.

Thanks for the welcome

 

[Recep İpek]

Merhaba! ripek, Tanıştığımıza memnun oldum.

:dusun:

 

[Haluk]

unfortunateley all software such as Exel that depend/use the IEEE
floating point standard will yield only up to 15 decimal places. Even with this
"accuracy", many numbers are represented as an approximation of their "true" value.

Yes, this is the exact definition of the problem.

Such as calculating, 170!

http://www.google.com/search?hl=en&q=170!&btnG=Google+Search

BTW, because of this problem (I guess) we can not calculate 171! with our microcomputers.

p.s. Ivan, Nice to see you on the board. :hey:

 

[Levent Menteşoğlu]

Mr Moala, welcome, nice to see you on our board.