Principle Of Mathematical Induction Question 49

Question: If n is a natural number, then

Options:

A) $ 1^{2}+2^{2}+…+n^{2}<\frac{n^{3}}{3} $

B) $ 1^{2}+2^{2}+…+n^{2}=\frac{n^{3}}{3} $

C) $ 1^{2}+2^{2}+…+n^{2}>n^{3} $

D) $ 1^{2}+2^{2}+…+n^{2}>\frac{n^{3}}{3} $

Show Answer

Answer:

Correct Answer: D

Solution:

  • [d] By taking option (d) When n = 1 then $ 1>\frac{1}{3} $ [true] When n = 2 then $ 5>\frac{8}{3}, $ [true] When n = 3 then $ 14>9, $ [true] When n = 4 then $ 30>\frac{64}{3}=21.33 $ [true]