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Author: Tinku Tara

p-n-n-th-prime-number-p-1-2-p-2-3-p-3-5-Does-the-following-converge-i-1-p-i-p-i-1-Prove-disprove-

Question Number 8661 by FilupSmith last updated on 20/Oct/16 $${p}_{{n}} ={n}^{{th}} \:\mathrm{prime}\:\mathrm{number} \\ $$$${p}_{\mathrm{1}} =\mathrm{2},\:{p}_{\mathrm{2}} =\mathrm{3},\:{p}_{\mathrm{3}} =\:\mathrm{5},\:… \\ $$$$ \\ $$$$\mathrm{Does}\:\mathrm{the}\:\mathrm{following}\:\mathrm{converge}: \\ $$$$\underset{{i}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{{p}_{{i}}…

nice-calculus-calculate-F-0-te-t-sin-3-t-dt-

Question Number 139734 by mnjuly1970 last updated on 30/Apr/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…..\:{nice}\:…{calculus}….. \\ $$$$\:\:\:\:\:\:\:{calculate}\:::\:\: \\ $$$$\:\:\:\:\:\:\mathscr{F}\::=\:\int_{\mathrm{0}} ^{\:\infty} {te}^{−{t}} {sin}^{\mathrm{3}} \left({t}\right){dt}=? \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:………………….. \\ $$ Answered…

Question-8653

Question Number 8653 by tawakalitu last updated on 19/Oct/16 Answered by prakash jain last updated on 19/Oct/16 $$\mathrm{2sin}\:{x}+\mathrm{3cos}\:{y}=\mathrm{5} \\ $$$$\mathrm{sin}\:{x}\leqslant\mathrm{1} \\ $$$$\mathrm{cos}\:{y}\leqslant\mathrm{1} \\ $$$$\mathrm{If}\:\mathrm{2sin}\:{x}+\mathrm{3cos}\:{y}=\mathrm{5} \\…