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- #1

#### Albert

##### Well-known member

- Jan 25, 2013

- 1,225

+2\times 4\times 6\times---\times 2000\times 2002$

is a multiple of 2003

- Thread starter Albert
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- Thread starter
- #1

- Jan 25, 2013

- 1,225

+2\times 4\times 6\times---\times 2000\times 2002$

is a multiple of 2003

- May 31, 2013

- 118

(2003-1)(2003-3)......(2003-2001) hence every term in the expansion contains 2003 exept the last term that is (1*3*5*....2001)(-1)^1001 hence it is negative and it cancel's out the first part of the question and hence 2003 divides every term ..

hence proved

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- #3

- Jan 25, 2013

- 1,225

perfect