(a) Work out (1,1+8,1+8+27) and (1+8+27+64). Guess a formula for (sum_{r=1}^{n} r^{3}) and prove it. (b) Check...

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(a) Work out $1,1+8,1+8+27$ and $1+8+27+64$. Guess a formula for $\sum_{r=1}^{n} r^{3}$ and prove it.

(b) Check that $1=0+1,2+3+4=1+8$ and $5+6+\cdots+9=8+27$. Find a general formula for which these are the first three cases. Prove your formula is correct.

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A Concise Introduction To Pure Mathematics

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Authors: Martin Liebeck

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Question Posted: May 19, 2024 12:00 PM

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(a) Work out (1,1+8,1+8+27) and (1+8+27+64). Guess a formula for (sum_{r=1}^{n} r^{3}) and prove it. (b) Check...

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A Concise Introduction To Pure Mathematics

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