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Question

Consider the following statements:
(1) The sum of cubes of first 20 natural numbers is 44400.
(2) The sum of squares of first 20 natural numbers is 2870.
Which of the above statements is/are correct?

A
(1) only
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B
(2) only
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C
Both (1) and (2)
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D
Neither (1) nor (2)
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Solution

The correct option is B (2) only
Sum of cubes of first n consecutive natural numbers is given by (n(n+1)2)2
Putting n=20, we have sum =(20(20+1)2)2=44100
Sum of squares of first n consecutive natural numbers is given by n(n+1)(2n+1)6
Putting n=20, we have the sum=20(20+1)(2×20+1)6=2870
Hence, option B is correct

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