What will be the value of {\sqrt3-1}/\sqrt3 +{\sqrt 5-\sqrt 3}/\sqrt15+{\sqrt 7-\sqrt 5}/\sqrt35 + .......+\frac{\sqrt2n+1-\sqrt2n- 1}{\sqrt4n^2-1} ?

Correct Answer is : 2n+1−12n+1

\sqrt{2 n+1}- 1 }/\sqrt{2n- 1 }

{\sqrt {2n- 1}- 1}/\sqrt{ 2n- 1 }

SSC CPO SI and ASI Model Paper 9

Question : 146 of 200

Marks: +1, -0

What will be the value of

{√3-1}/√3 +{√ 5-√ 3}/√15+{√ 7-√ 5}/√35 + .......+{√2n+1-√2n- 1}/{√4n^2-1} ?

Solution:

3) The given expression can bewritten as

1- 1/√3+√ 5/√15-√ 3/√15+√ 7/√35-√5/√35+.......+{√{2n+1}}/{√{4n^2- 1}}-√{2n-1}/{√{4n^2- 1}}

=1- 1/√3+ 1/√3- 1/√5+1/√5

-1 /√7+.........+1/√{2n -1}-1/√{2n +1}

=1 -1/ √{2n+ 1} ={√{2n+ 1 }- 1}/√{2n+ 1 }

Go to Question:

Prev Question

Next Question