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How do I answer this without using a calculator?

$$\sum_{x=1}^{20}8x^{3}$$

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2 Answers

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For this question you can use the formula

$$\sum_{x=1}^{n}x^{3}=(\frac{n(n+1)}{2})^{2}$$

Using this formula where n = 20 you get 44100. Then you multiply by 8 to get 352800.

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$$\sum_{x=1}^{20}8x^{3}=8\sum_{x=1}^{20}x^{3}=8(1^3+2^3+3^3+...+20^3)=8(44100)=352800$$

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