on Tuesday, January 20, 2009

The answer to squared numbers are as follow :

Firstly, you need to know the formula 1*1 + 2*2 + 3*3 + ......+ x*x = x/6(x+1)(2x+1)

Then, 1*1 + 3*3 + ...... + 99*99 = (1*1 + 2*2 + 3*3 +...... + 100*100 ) - (2*2 + 4*4 + ......
100*100 )
= [ (100/6) (100+1) (2*100+1) ]-[ 2*2 ( 1*1 + 2*2 + 3*3 +......
50*50) ]
= 338350 - [4 * (50/6) (50+1) (2*50+1)
= 338350 - 171700
= 166650

1 comments:

Kenneth said...

Oh, I understand now. Mathsguy is so godlike! xD

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