Question : If Un = $\frac{1}{n}-\frac{1}{n+1}$, then the value of U1 + U2 + U3 + U4 + U5 is:
Option 1: $\frac{1}{4}$
Option 2: $\frac{5}{6}$
Option 3: $\frac{1}{6}$
Option 4: $\frac{1}{3}$
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Correct Answer: $\frac{5}{6}$
Solution : U n = $\frac{1}{n}-\frac{1}{n+1}$ So, U 1 = $\frac{1}{1}-\frac{1}{1+1}=1-\frac{1}{2}$ Similarly, U 2 = $\frac{1}{2}-\frac{1}{3}$ U 3 = $\frac{1}{3}-\frac{1}{4}$ U 4 = $\frac{1}{4}-\frac{1}{5}$ U 5 = $\frac{1}{5}-\frac{1}{6}$ Adding all this we get, U 1 + U 2 + U 3 + U 4 + U 5 = $1-\frac{1}{6}=\frac{5}{6}$ Hence, the correct answer is $\frac{5}{6}$.
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