Question

The value of 1/1+√2 + 1/√2+√3 + 1/√3+√4 +1/√4+√5 + 1/√5+√6 + 1/√6+√7+1/√7+√8+1/√8+√9 is _
Option:
1) 0
2) 1
3) 2
4) 4
Tell me the correct option with explaination pls.

Answer 1

Final Answer : 2

Steps:
1) Rationalize all the terms individually.
2)After, rationalization denominator becomes 1 , then add all terms.
3) On adding one element of consecutive terms gets cancelled out.
4) Finally, remains (√9 -1 )/ 1= 2

Answer 2

The value of 1/1+√2 + 1/√2+√3 + 1/√3+√4 +1/√4+√5 + 1/√5+√6 + 1/√6+√7+1/√7+√8+1/√8+√9 is 1