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Question Number 172688 by mr W last updated on 30/Jun/22

(1+2+3+4)^2 =1^2 +2^2 +3^2 +4^2   right?  (1+2+3+4)^2 =1^3 +2^3 +3^3 +4^3   right?

$$\left(\mathrm{1}+\mathrm{2}+\mathrm{3}+\mathrm{4}\right)^{\mathrm{2}} =\mathrm{1}^{\mathrm{2}} +\mathrm{2}^{\mathrm{2}} +\mathrm{3}^{\mathrm{2}} +\mathrm{4}^{\mathrm{2}} \:\:{right}? \\ $$$$\left(\mathrm{1}+\mathrm{2}+\mathrm{3}+\mathrm{4}\right)^{\mathrm{2}} =\mathrm{1}^{\mathrm{3}} +\mathrm{2}^{\mathrm{3}} +\mathrm{3}^{\mathrm{3}} +\mathrm{4}^{\mathrm{3}} \:\:{right}? \\ $$

Commented by Rasheed.Sindhi last updated on 30/Jun/22

(1+2+3+4)^2 =1^2 +2^2 +3^2 +4^2          False  (1+2+3+4)^2 =1^3 +2^3 +3^3 +4^3         True

$$\left(\mathrm{1}+\mathrm{2}+\mathrm{3}+\mathrm{4}\right)^{\mathrm{2}} =\mathrm{1}^{\mathrm{2}} +\mathrm{2}^{\mathrm{2}} +\mathrm{3}^{\mathrm{2}} +\mathrm{4}^{\mathrm{2}} \: \\ $$$$\:\:\:\:\:\:{False} \\ $$$$\left(\mathrm{1}+\mathrm{2}+\mathrm{3}+\mathrm{4}\right)^{\mathrm{2}} =\mathrm{1}^{\mathrm{3}} +\mathrm{2}^{\mathrm{3}} +\mathrm{3}^{\mathrm{3}} +\mathrm{4}^{\mathrm{3}} \: \\ $$$$\:\:\:\:\:{True} \\ $$

Commented by mr W last updated on 30/Jun/22

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Commented by mahdipoor last updated on 30/Jun/22

1^3 +2^3 +...+a^3 =(((a(a+1))/2))^2 =(1+2+...+a)^2

$$\mathrm{1}^{\mathrm{3}} +\mathrm{2}^{\mathrm{3}} +...+{a}^{\mathrm{3}} =\left(\frac{{a}\left({a}+\mathrm{1}\right)}{\mathrm{2}}\right)^{\mathrm{2}} =\left(\mathrm{1}+\mathrm{2}+...+{a}\right)^{\mathrm{2}} \\ $$

Commented by mr W last updated on 30/Jun/22

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