JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

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The sum of the first

n

terms of the series

\frac{1}{{\sqrt 2 + \sqrt 5 }} + \frac{1}{{\sqrt 5 + \sqrt 8 }} + \frac{1}{{\sqrt 8 + \sqrt {11} }} + \;...

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Correct option: A

\frac{1}{3}\left( {\sqrt {3n + 2} - \sqrt 2 } \right)

Option A (1/3(√(3n+2) - √2)) is correct because it is the simplified sum of the series after rationalizing the denominator.

More Questions from SEQUENCE OF SERIES

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A=\{1,2,3\}, B=\{3,4\}, C=\{4,5,6\}

{A} \cup({B} \cap {C})

A-(B \cap C)

(B \cup C)-A

a,b,c

a,x,b

b,y,c

{x^2},{b^2},{y^2}

P(x)=1-x+x^2-x^3+\ldots+x^{2012}

y

Q(y)=a_0+a_1 y+\ldots+a_{2012} y^{2012}

y=x-2

\sum\limits_{{i=0}}^{2012} a_i

\log \left(\frac{5 c}{a}\right), \log \left(\frac{3 b}{5 c}\right)

\log \left(\frac{a}{3 b}\right)

A P

a, b

G P

a, b, c

\frac{3}{4}