NIMCET 2015 Question Paper with solutions

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Question : 23 of 120

Marks: +1, -0

The value of the sum

1/{2√1+1√2}

+

1/{3√2+2√3}

+

1/{4√3+3√4}

+ ... +

1/{25√{24}+24√{25}}

is :

9/10
4/5
14/15
7/15

Solution:

We have,

1/{2√1+1√2}+1/{3√2+2√3}+1/{4√3+3√4}+...+1/{25√{24}+24√{25}}

Now,

T_n=1/{(n+a)√n+n√n+1}

⇒T_n=1/{√n√n+1(√n+1+√n)}

⇒T_{n}={√{n}+1-√{n}}/{√{n}√{n}+1}={1}/{√{n}}-{1}/{√{n+1}}

S={1}/{√{1}}-{1}/{√{2}}+{1}/{√{2}}-{1}/{√{3}}{1}/{√{24}}-{1}/{√{25}}

=1-{1}/{√{25}}=1-{1}/{5}={4}/{5}

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