# What will be the Value of the Equation? If

If u_{n} = 1/n – 1/n+1 then the value of u_{1}+u_{2}+u_{3}+u_{4}+u_{5} is

- 1/2
- 1/3
- 2/5
- 5/6

**Answer: (4) 5/6**

**Explanation:-**

U_{n} = 1/n – 1/(n + 1) (Given)

Then,

U_{1} = 1- 1/ 2, U_{2} = 1/2 – 1/3, U_{3} = 1/3 – 1/ 4, U_{4} = 1/4 – 1/5,

U_{5} = 1/5 – 1/6

Then,

U_{1} + U_{2} + U_{3} + U_{4} + U_{5} = 1 – 1/2 + 1/2 – 1/3 + 1/3 – 1/4 + 1/4 – 1/5 + 1/5 – 1/6

= 1- 1/6

= (6 – 1)/6 = 5/6

Hence, the answer is (4) 5/6.