I am evaluating the following summation, $$\sum_{r=0}^9 (r^3 - 1)$$ and I have gotten $$\sum_{r=1}^9 r^3 - \sum_{r=1}^91 = \frac{1}{4} \cdot 9^2 \cdot (9+1)^2 - 9 = 2016$$ Is this the correct way to express my solution? Please correct me if there are any mistakes.
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1Small error, $\sum_0^9 1=10$. – André Nicolas Oct 09 '15 at 16:49
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The answer's nearly correct, but the title isn't appropriate. – Oct 09 '15 at 16:50
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@AndréNicolas there was a typing error. I actually converted r=0 into r=1 so does that mean I should use $\sum_{r=1}^{10} 1 = 10$ instead? – Lily L Oct 09 '15 at 16:53
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1Yes, if you like $\sum_{r=0}^9 1=\sum_{s=1}^{10}$. In either case you are adding up ten $1$'s and get $10$. – André Nicolas Oct 09 '15 at 16:59
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Alright. Thanks a lot! – Lily L Oct 09 '15 at 17:06
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It should be, $$\sum_{r=1}^9 r^3 - \sum_{r=1}^{10}1 = \frac{1}{4}\cdot9^2\cdot(9+1)^2 - 10 = 2015$$
Since $$\sum_{r=0}^91 = \sum_{r=1}^{10} 1 $$ not $$\sum_{r=0}^91 = \sum_{r=1}^91$$
Lily L
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