# How do you find the sum of the digits of number N? Say N = 10

1. Jan 12, 2004

### PrudensOptimus

How do you find the sum of the digits of number N?

Say N = 10

2. Jan 12, 2004

### BigRedDot

If memory serves me correctly:

$$\sum_{k=1}^N k= \frac{N(N+1)}2$$

a fact that you would prove by induction.

3. Jan 13, 2004

### HallsofIvy

Staff Emeritus
Was that what was meant? The "sum of the digits" of 10 is 1+ 0= 1, of course.

4. Jan 13, 2004

### himanshu121

It will be true only if the digits form a Arithmetic Projection
for eg N=2468 etc {2+4+6+8}
but not in general say for N=12245 {1+2+2+4+5}

5. Jan 13, 2004

### BigRedDot

You're right, I answered a completely different question. Well, I am sure someone asked my question somewhere, sometime. :)

6. Jan 13, 2004

### PrudensOptimus

Yea what if N = 1231247839783924723840723084732084738274... + ... N?

7. Jan 14, 2004

### himanshu121

Ofcourse it would be
as N=1+0
here it will be N=1+2+3+1+2+4+7+8+3+9+7+8+3+9+2+4+7+2+3+8+4+0+7+2+3+0+8+4+7+3+2+0+8+4+7+3+8+2+7+4+...+x+y+z+a+b+c+d