Which pages are missing?

[ashitpro]

From a book, a number of pages are missing. The sum of the page numbers of these pages is 9808. Which pages are missing?

[arunmib]

I think multiple answers are there for this....

For eg:
1) page numbers 9806 + 2
2) page number 9800 + 8
3) page numbers 8 + 800 + 2000 + 3000 + 4000.....

Any corrections.... .

[ashitpro]

Missing pages are in sequence

[Darryl]

There are 32 pages missing starting with page 291

[ashitpro]

There are 32 pages missing starting with page 291

Dear genious
You always has the answer
But,please tell us the method

[Darryl]

Dear genious
You always has the answer
But,please tell us the method

It's because you only ask for the answer, and I am not that good(clear) at explaining.
**Edit** another reason is to give others a chance to figure it out...for all they know I could be wrong

It's just algebra, more or less.

Let X = a page number
Therefore X + 1 = the next consecutive page, x+2, the page after that X+n = the last page and n+1 = total number of pages

If two pages were missing the equation would be

x + (x+1) = 9808
2x + 1 = 9808
2x = 9807
x = 4903.5 which obviously is wrong since you can't be missing half a page( well you can, but you know what I mean)

3 pages would be
x + (x+1) + (x+2) = 9808
3x+3= 9808
4 would be
x + (x+1) + (x+2) + (x+3) = 9808
4x+6

see the pattern of the second nomial? It's a simple arithmetic sequence:
F(n) = Sum (0...N)
and how it relates to the coefficient of the first?

So a general formula can be create thus:
nX + F(n-1) = 9808
nX = 9808 - F(n-1)
X = (9808-F(n-1)) / n

n = number of pages
X = begining page

I used trial and error to get the correct n, (did it in an excel spreadsheet)

[jkmyoung]

Each sheet of paper has 2 pages or sides.
Note that when you open a book in between 2 pages, an even number should be on the left, an odd on the right, for a traditional book.
So for a single piece of paper, it will have odd page first then even.

Let the page number be
2n+1, for some whole number n
2n+2, is the other side.
The next sheet would have
2n+3,
2n+4,

If x sheets were ripped out, we would get,

(2n+1) + (2n+2) + (2n+3) + (2n+4) + (2n+5) + (2n+6) + ... + (2n+2x - 1) + (2n + 2x)
regrouping, we get:
= (2n+1 + 2n+2x)*x
= (4n + 2x + 1) * x

Factoring 9808, we get:
2*2*2*2*613
(4n+2x+1) is odd
(4n+2x+1) = 613
-> x = 16

(4n+32+1) = 613.
4n = 580
n = 145

->2n+1 = 291
2n+2x = 322

Pages 291 -> 322 were ripped out

Note that even if you do not make the assumption that we start on an odd number, we'll still get the same result.