If F(X) = 1/X – 1/(X+1), What is the sum of F(1)+F(2)+F(3)+F(4)+…….+F(100)?
A. 98/101
B. 99/101
C. 100/101
D 102/101
E. 103/101
A. 98/101
B. 99/101
C. 100/101
D 102/101
E. 103/101
F(1) = 1-1/2
F(2) = 1/2-1/3
F(3) = 1/3-1/4
.
.
.
.
F(100)= 1/100-1/101
We observe that all terms get cancelled
Thus we finally we have
1-1/101 = 100/101
Answer C
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