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Category: Arithmetic

a-b-c-d-e-kids-are-in-ascending-order-of-heights-If-they-are-to-stand-in-a-circle-in-a-way-so-that-the-sum-of-difference-in-heights-of-adjacent-pairs-is-a-minimum-find-this-minimum-

Question Number 155797 by ajfour last updated on 09/Oct/21 $${a},{b},{c},{d},{e}\:\:\left({kids}\right)\:{are}\:{in}\:{ascending} \\ $$$${order}\:{of}\:{heights}.\:{If}\:{they}\:{are} \\ $$$${to}\:{stand}\:{in}\:{a}\:{circle}\:{in}\:{a}\:{way}\:{so} \\ $$$${that}\:{the}\:{sum}\:{of}\:\mid{difference}\:{in} \\ $$$${heights}\:{of}\:{adjacent}\:{pairs}\mid \\ $$$$\:{is}\:{a}\:{minimum},\:{find}\:{this} \\ $$$$\:{minimum}. \\ $$ Commented…

Let-T-k-is-the-k-th-term-and-S-k-is-the-sum-of-the-first-k-term-in-arithmetic-progression-If-T-3-T-6-T-9-T-12-T-15-T-18-45-Find-S-20-

Question Number 24677 by Joel578 last updated on 24/Nov/17 $$\mathrm{Let}\:{T}_{{k}} \:\mathrm{is}\:\mathrm{the}\:{k}^{\mathrm{th}} \:\mathrm{term}\:\mathrm{and}\:\mathrm{S}_{{k}} \:\mathrm{is}\:\mathrm{the}\:\mathrm{sum} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{first}\:{k}\:\mathrm{term}\:\mathrm{in}\:\mathrm{arithmetic}\:\mathrm{progression} \\ $$$$\mathrm{If}\:{T}_{\mathrm{3}} \:+\:{T}_{\mathrm{6}} \:+\:{T}_{\mathrm{9}} \:+\:{T}_{\mathrm{12}} \:+\:{T}_{\mathrm{15}} \:+\:{T}_{\mathrm{18}} \:=\:\mathrm{45} \\ $$$$\mathrm{Find}\:{S}_{\mathrm{20}}…

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Question Number 90009 by M±th+et£s last updated on 20/Apr/20 $$\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\left(\sqrt{\mathrm{2}}−\mathrm{1}\right)^{\mathrm{2}{n}+\mathrm{1}} }{\left(\mathrm{2}{n}+\mathrm{1}\right)^{\mathrm{2}} }=? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

1-2-1-3-2-2-3-5-3-2-5-7-n-2-2n-1-2n-1-

Question Number 155465 by cortano last updated on 01/Oct/21 $$\frac{\mathrm{1}^{\mathrm{2}} }{\mathrm{1}×\mathrm{3}}+\frac{\mathrm{2}^{\mathrm{2}} }{\mathrm{3}×\mathrm{5}}+\frac{\mathrm{3}^{\mathrm{2}} }{\mathrm{5}×\mathrm{7}}+…+\frac{\mathrm{n}^{\mathrm{2}} }{\left(\mathrm{2n}−\mathrm{1}\right)\left(\mathrm{2n}+\mathrm{1}\right)}= \\ $$ Answered by Ar Brandon last updated on 03/Oct/21 $${S}=\underset{{k}=\mathrm{1}}…