If a1, a2, ... are in A.P., then, 1a1+a2 + 1a2+a3 + ... + 1an+an+1 is equal to
Explanation:
The best approach to solving such questions in exams is to put values and then cross checking the options.
Let n = 2, so we will have three terms in AP (a1, a2 and a3). Let a1 = a2 = a3 = 1.
1/(√a1 + √a2) = 1/2.
1/(√a2 + √a3) = 1/2.
∴ [1/(√a1 + √a2)] + [1/(√a2 + √a3)] = (1/2) + (1/2) = 1.
Put n = 2 in;
Option 1: 2/0 = not defined. So this option is incorrect.
Option 2: 2/(1 + 1) = 2/2 = 1. So this option is correct.
Option 3: (2 − 1)/(1 + 1) = 1/2. So this option is incorrect.
Option 4: (2 − 1)/(1 + 1) = 1/2. So this option is incorrect.
Hence, option (b).
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