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Category: Geometry

If-they-said-that-k-1-k-diverges-why-1-2-3-4-1-12-

Question Number 9436 by geovane10math last updated on 08/Dec/16 $$\mathrm{If}\:\mathrm{they}\:\mathrm{said}\:\mathrm{that}\:\underset{{k}=\mathrm{1}} {\overset{\infty} {\sum}}\:{k}\:\mathrm{diverges},\:\mathrm{why} \\ $$$$\mathrm{1}\:+\:\mathrm{2}\:+\:\mathrm{3}\:+\:\mathrm{4}\:+\:…\:=\:−\:\frac{\mathrm{1}}{\mathrm{12}}\:? \\ $$ Answered by mrW last updated on 08/Dec/16 $$\:\:\:\mathrm{T}=\mathrm{1}−\mathrm{2}+\mathrm{3}−\mathrm{4}+\mathrm{5}−\mathrm{6}+… \\…

Question-140373

Question Number 140373 by mr W last updated on 06/May/21 Commented by mr W last updated on 06/May/21 $${find}\:{the}\:{radius}\:{of}\:{the}\:{smallest}\: \\ $$$${hollow}\:{sphere}\:{which}\:{can}\:{hold} \\ $$$${four}\:{balls}\:{with}\:{radii}\:{a},{b},{c}\:{and}\:{d}\: \\ $$$${respectively}\:{inside}.…

The-gamma-function-s-0-e-x-x-s-1-dx-How-to-calculate-the-gamma-function-in-an-easy-and-not-time-consuming-way-

Question Number 9233 by geovane10math last updated on 24/Nov/16 $$\mathrm{The}\:\mathrm{gamma}\:\mathrm{function}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Gamma\left({s}\right)\:=\:\int_{\mathrm{0}} ^{\infty} {e}^{−{x}} {x}^{{s}−\mathrm{1}} \:{dx} \\ $$$$\mathrm{How}\:\mathrm{to}\:\mathrm{calculate}\:\mathrm{the}\:\mathrm{gamma}\:\mathrm{function} \\ $$$$\mathrm{in}\:\mathrm{an}\:\mathrm{easy}\:\mathrm{and}\:\mathrm{not}\:\mathrm{time}-\mathrm{consuming}\: \\ $$$$\mathrm{way}? \\ $$$$ \\…

Question-74748

Question Number 74748 by mr W last updated on 30/Nov/19 Commented by mr W last updated on 30/Nov/19 $${If}\:{the}\:{total}\:{area}\:{of}\:{red}\:{squares}\:{is}\:{A}. \\ $$$${Find}\:{the}\:{total}\:{area}\:{of}\:{the}\:{blue}\:{squares} \\ $$$${and}\:{that}\:{of}\:{the}\:{green}\:{squares}. \\ $$$$…