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 :

• A. Both Statement I and Statement II are true
• B. Both Statement I and Statement II are false
• C. Statement I is true but statement II is false
• D. Statement I is false but statement II is true

Answer 1

Answer: (D)

Statement I is false but statement II is true

Answer 2

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