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: $\frac{1}{3}$
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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