CAT 2019 Progression Question (Hard)

Question

If are in Arithmetic Progression A.P. , then the value of the expression is equal to

Accepted Answer

Step 1 Given in A.P. Expression 1 a a 1 a a ... 1 a a Step 2 Multiply each term by a a a a Each becomes a a a a Sum becomes a telescoping sum a a a a ... a a d a a d There are n terms, each with denominator d So Sum n a a Final Answer The value is n a a

CAT 2019

Quantitative

Progression

Hard

If $a_1, a_2, \ldots$ are in Arithmetic Progression (A.P.), then the value of the expression

$\dfrac{1}{\sqrt{a_1} + \sqrt{a_2}} + \dfrac{1}{\sqrt{a_2} + \sqrt{a_3}} + \cdots + \dfrac{1}{\sqrt{a_n} + \sqrt{a_{n+1}}}$
is equal to:

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