 All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars  perplexus dot info  Front to back (Posted on 2007-03-18) Suppose one sequence is formed by multiplying termwise the sequence 1,2,...n by the sequence n,n-1,...1 and another sequence is formed by multiplying termwise the sequence 2,4,...n by the sequence 2,4,...n.

Show that for even n, the sum of each sequence is the same.

 No Solution Yet Submitted by Gamer No Rating Comments: ( Back to comment list | You must be logged in to post comments.) Lots of summing | Comment 1 of 3
Writing n=2K, the first sum is the sum for I=1 to K of I times (2K+1-I), or (2K+1) times the sum of all numbers from 1 to 2K, minus the sum of the squares of all numbers from 1 to 2K, which eventually works out to 2/3.K.(K+1).(2K+1).

The second sum is 4 times the sum of squares of the numbers from 1 to K, which comes out to the same value.

 Posted by Old Original Oskar! on 2007-03-18 13:14:50 Please log in:

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