In first bracket, there is 1 * 2 in the denominator.
In the second bracket, there is 2*3 in the denominator
In the third bracket, there will be 3*4 in the denominator.
And in the last bracket, there is 2007*2008 in the denominator.
So, no of terms are from 1 to 2007 (2007 terms) or from 2 to 2008 (still 2007 terms).
So, 1+1+1+1+1+…(2007 times) = 2007
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