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Question

The sum of series 13+23+33+....+153 is


A

22000

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B

10000

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C

14400

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D

15000

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Solution

The correct option is C

14400


Explanation for the correct answer:

The sum of the cubes of the first n natural numbers is given as

13+23+33+.......+n3=n2n+124

Here we have n=15

Hence, the sum of the cubes of the first 15 natural numbers is given as

13+23+33+....+153=15215+124

=225×2564

=576004

⇒ 13+23+33+....+153=14400

Hence, the sum of the series, 13+23+33+....+153 is 14400.

Hence, option C is the correct answer.


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