Which is the integer part of the number N = 1/(1*2)+1/(2*3)+1/(3*4)+.....+1/(2007*2008)?

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neela | High School Teacher | (Level 3) Valedictorian

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Given N= 1/(1*2)+1/(2*3)+(1/3*4)+.......+1/2007*2008.

Each term on the right is of the form 1/(r*(r+1))=1/r-1/(r+1).

Therefore,splitting each term in this form we get,


Rearranging we get,




= 2007/2008


Therefore,the integer part of the N is 0

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