The value of $(1^{3} + 2^{3} + 3^{3} + . . . . . . . 15^{3}) - (1 + 2 + 3 + . . . 15)$ is:

14280

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14400

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12280

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13280

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Solution

The correct option is A $14280$
$(1^{3} + 2^{3} + 3^{3} + . . . . . . {.15}^{3}) (1 + 2 + 3 + . . .15)$
Sum of cubes= ${\frac{n \times (n + 1)}{2}}^{2}$
Sum of the AP : $\frac{n (n + 1)}{2}$
= ${\frac{15 (15 + 1)}{2}}^{2} - \frac{15 \times 16}{2}$
= ${\frac{16 \times 15}{2}}^{2} - 15 \times 8$
= ${15 \times 8}^{2} - 15 \times 8$
$= 14400 - 120$
$= 14280$

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Similar questions

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

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

\frac{1^{3}}{1} + \frac{1^{3} + 2^{3}}{2} + \frac{1^{3} + 2^{3} + 3^{3}}{3} + . . . n

=

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