2- 2- 2- 3- 3- 13 - 23- 32- 13 is equal to

The correct option is D 936 936 = 2× 2× 2× 3× 3× 13 = 2^3× 3^2× 13 Therefore , D is the correct answer. ...

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Fundamental Theorem of Arithmetic

2× 2× 2× 3× 3...

Question

$2 \times 2 \times 2 \times 3 \times 3 \times 13 = 2^{3} \times 3^{2} \times 13$ is equal to

1004

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828

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724

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936

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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)

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

100 S_{n} = n

n

\frac{\frac{1}{2} . \frac{2}{2}}{1^{3}} + \frac{\frac{2}{2} . \frac{3}{2}}{1^{3} + 2^{3}} + \frac{\frac{3}{2} . \frac{4}{2}}{1^{3} + 2^{3} + 3^{3}} + . . . .

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