Solve- 12 3- 13 3- 56 3

According to the problem, ( 12)^3 + ( 13)^3 ( 56)^3 = 18 + 127 + 125216 = 27 + 8 + 125216 = 160216 = 0.740 ...

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Addition of Fractions

Solve:- 12 ...

Question

Solve:-
${(\frac{1}{2})}^{3} + {(\frac{1}{3})}^{3} - {(\frac{5}{6})}^{3}$

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Solution

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Write the value of ${(\frac{1}{2})}^{3} + {(\frac{1}{3})}^{3} - {(\frac{5}{6})}^{3}$

Without actually calculating the cubes, find the value of :

{(\frac{1}{2})}^{3} + {(\frac{1}{3})}^{3} + {(\frac{- 5}{6})}^{3}

{(\frac{1}{2})}^{3} + {(\frac{1}{3})}^{3} - {(\frac{5}{6})}^{3}

1^{3} + 2^{3} + 3^{3} + . . . + n^{3} = \frac{1}{4} n^{2} (n + 1)^{2}

\sum_{r = 1}^{n} \frac{1^{3} + 2^{3} + 3^{3} + . . . + r^{3}}{r (r + 1)}

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