Given below are two statements: Statement I: For n ≥1, we have $\frac{1}{1·2}+\frac{1}{2·3}+\frac{1}{3·4}+.....+\frac{1}{n(n+1)}=\frac{n^2}{n+1}$ Statement II: (1+x) n ≥ (1+nx) for all natural number n, where x -1. In the light of the above Statements, choose the most appropriate answer from the options given below :

Question

Given below are two statements: Statement I: For n ≥1, we have $\frac{1}{1·2}+\frac{1}{2·3}+\frac{1}{3·4}+.....+\frac{1}{n(n+1)}=\frac{n^2}{n+1}$ Statement II: (1+x) n ≥ (1+nx) for all natural number n, where x > -1. In the light of the above Statements, choose the most appropriate answer from the options given below :

cdquestions Admin · Accepted Answer

The correct answer is(D): Statement I is false but statement II is true

Answer

Both Statement I and Statement II are true

Answer

Both Statement I and Statement II are false

Answer

Statement I is true but statement II is false

Answer

Statement I is false but statement II is true

The Correct Option is D

Solution and Explanation

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