The sum of the series $1^{3} - 2^{3} + 3^{3} - \dots \dots + 9^{3} = ?$

300

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125

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425

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0

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Solution

The correct option is B $300$
$1^{3} - 2^{3} + 3^{3} - 4^{3} . . . . . . + 9^{3}$
$= 1^{3} + 3^{3} + 5^{3} + . . . . . . 9^{3} - (2^{3} + 4^{3} + 6^{3} + . . . . . . 8^{3})$
$= 1 + 27 + 125 + 343 + 729 - (8 + 64 + 216 + 512)$
$= 1225 - 800$
$= 425$

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1^{3} - 2^{3} + 3^{3} - . . . . . . . . . + 9^{3} =

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