Question Number 195114 by mustafazaheen last updated on 24/Jul/23
$$ \\ $$$$\:\:\:\:\: \\ $$$$\:\:\:\:\:\underset{\mathrm{k}=\mathrm{3}} {\overset{\mathrm{55}} {\sum}}\mathrm{k}=? \\ $$$$\left.\mathrm{1}\left.\right)\left.\mathrm{5}\left.\mathrm{5}\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{2}\right)\mathrm{9k}\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{3}\right)\mathrm{53k}\:\:\:\:\:\:\:\:\:\:\:\mathrm{4}\right)\mathrm{45} \\ $$$$ \\ $$$$ \\ $$
Answered by cortano12 last updated on 25/Jul/23
$$\:\:\underset{{k}=\mathrm{3}} {\overset{\mathrm{55}} {\sum}}\:{k}\:=\:\underset{{k}=\mathrm{1}} {\overset{\mathrm{55}} {\sum}}{k}−\underset{{k}=\mathrm{1}} {\overset{\mathrm{2}} {\sum}}{k} \\ $$$$\:\:\:=\:\frac{\mathrm{55}×\mathrm{54}−\mathrm{2}×\mathrm{1}}{\mathrm{2}}=\mathrm{55}×\mathrm{27}−\mathrm{1} \\ $$
Answered by JDamian last updated on 25/Jul/23
$$\mathrm{3}+\mathrm{4}+\centerdot\centerdot\centerdot+\mathrm{54}+\mathrm{55}=\frac{\mathrm{3}+\mathrm{55}}{\mathrm{2}}×\mathrm{53} \\ $$