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Consider the following assertions: Assertion 1: For every natural number n \u2265 2, 1/\u221a1 + 1/\u221a2 + ... + 1/\u221an > \u221an. Assertion 2: For every natural number n \u2265 2, \u221a(n(n + 1)) < n + 1.

1. Assertion 1 is false, and Assertion 2 is true.
2. Assertion 1 is true, Assertion 2 is true, and Assertion 2 correctly explains Assertion 1.
3. Assertion 1 is true, Assertion 2 is true, but Assertion 2 does not correctly explain Assertion 1.
4. Assertion 1 is true, and Assertion 2 is false.

Correct answer: Assertion 1 is true, Assertion 2 is true, but Assertion 2 does not correctly explain Assertion 1.

Solution

Assertion 1 is true because the sum of the series diverges and grows faster than the square root function, while Assertion 2 is also true as it demonstrates a relationship between the square root of a product and a linear expression, but it does not provide a direct justification for the behavior of the series in Assertion 1.

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