Among the following relationships, which one is INCORRECT?
Sum of cubes of first n natural numbers = [Sum of first n natural numbers]$^{2}$
Sum of first n even numbers = Sum of first n odd numbers + n
Sum of first n natural numbers = 2 × Sum of first n even numbers
Sum of squares of first n natural numbers = 2 × Sum of squares of first n even numbers
Explanation:
Substitute the respective formulas in each option and check.
Sum of squares of first n natural numbers = n(n + 1)(2n + 1)/6
Sum of squares of first n even numbers = 2n(n + 1)(2n + 1)/3
Hence 4th option is incorrect, whereas all others are correct.