$T h e v a l u e o f (1^{3} + 2^{3} + 3^{3} + \dots + 15^{3}) - (1 + 2 + 3 + \dots + 15) i s$

14280

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14400

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14520

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14200

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Solution

The correct option is A 14280
$W e h a v e, 1^{3} + 2^{3} + 3^{3} + 4^{3} + 5^{3} + \dots + n^{3} = {(1 + 2 + 3 + 4 + 5 + \dots + n)}^{2} a n d S u m o f f i r s t n c o n s e c u t i v e n a t u r a l n u m b e r s = (\frac{n}{2}) (n + 1) A p p l y i n g t h i s w e g e t, = {(\frac{15 \times 16}{2})}^{2} - \frac{15 \times 16}{2} = {(120)}^{2} - 120 = 14400 - 120 = 14280$

Correct Option: c) 14280

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Similar questions

(1^{3} + 2^{3} + 3^{3} + . . . . . . . 15^{3}) - (1 + 2 + 3 + . . . 15)

1 + \frac{1^{3} + 2^{3}}{1 + 2} + \frac{1^{3} + 2^{3} + 3^{3}}{1 + 2 + 3} + \cdot \cdot \cdot + \frac{1^{3} + 2^{3} + 3^{3} + \cdot \cdot \cdot + 15^{3}}{1 + 2 + 3 + \cdot \cdot \cdot + 15} - \frac{1}{2} (1 + 2 + 3 + \cdot \cdot \cdot + 15)

1 + \frac{1^{3} + 2^{3}}{1 + 2} + \frac{1^{3} + 2^{3} + 3^{3}}{1 + 2 + 3} + \cdot \cdot \cdot + \frac{1^{3} + 2^{3} + 3^{3} + \cdot \cdot \cdot + 15^{3}}{1 + 2 + 3 + \cdot \cdot \cdot + 15} - \frac{1}{2} (1 + 2 + 3 + \cdot \cdot \cdot + 15)

The sum of $1^{3}$ + $2^{3}$ + $3^{3}$ + $4^{3}$ + ........... + $15^{3}$ is

\frac{1^{3} + 2^{3} + 3^{3} + \dots + 10^{3}}{1 + 2 + 3 + \dots + 10} =

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