Solve- -r-1n13-23-33-r3rr-1

[ ∑ #160; _ r=1 ^ n 1^ 3 + 2^ 3 + 3^ 3 +.......+ r^ 3 / r( r+1 ...

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Exponential Representation for Irrational Numbers

Solve: ∑r=1n...

Question

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

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Solution

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Similar questions

t_{r} = \frac{1^{2} + 2^{2} + 3^{2} + . . . + r^{2}}{1^{3} + 2^{3} + . . . + r^{3}}

S_{n} = n \sum r = 1 {(- 1)}^{r} . t_{r},

lim n \to \infty S_{n} = \frac{2}{3}

1^{2} + 2^{2} + 3^{2} + . . . + r^{2} = \frac{r (r + 1) (2 r + 1)}{6}

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

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

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

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

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

1^{3} + 2^{3} + 3^{3} + . . . . . . + 21^{3}

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