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Category: Algebra

The-sum-of-the-first-n-terms-of-a-series-is-given-by-S-n-n-2-7n-2-i-Find-a-formula-for-the-nth-term-ii-write-down-the-first-5-terms-of-the-sequence-

Question Number 76793 by necxxx last updated on 30/Dec/19 $${The}\:{sum}\:{of}\:{the}\:{first}\:{n}\:{terms}\:{of}\:{a}\:{series} \\ $$$${is}\:{given}\:{by}:\:{S}_{{n}} ={n}^{\mathrm{2}} +\mathrm{7}{n}+\mathrm{2}. \\ $$$$\left({i}\right){Find}\:{a}\:{formula}\:{for}\:{the}\:{nth}\:{term} \\ $$$$\left({ii}\right){write}\:{down}\:{the}\:{first}\:\mathrm{5}\:{terms}\:{of}\:{the} \\ $$$${sequence} \\ $$$$ \\ $$ Commented…

cos65-m-sin40-

Question Number 11258 by uni last updated on 18/Mar/17 $${cos}\mathrm{65}={m}\:\:\Rightarrow\:{sin}\mathrm{40}=? \\ $$ Answered by ajfour last updated on 18/Mar/17 $$\mathrm{let}\:\mathrm{p}=\mathrm{sin}\:\mathrm{40}\:=\mathrm{cos}\:\mathrm{50} \\ $$$$\:\:\mathrm{p}\:=\mathrm{sin}\:\mathrm{40}=\:\mathrm{1}−\mathrm{2sin}\:^{\mathrm{2}} \mathrm{25} \\ $$$$\mathrm{sin}\:\mathrm{25}\:=\:\mathrm{cos}\:\mathrm{65}\:=\mathrm{m}…

Given-that-a-1-b-gt-0-Prove-the-followings-1-1-2-a-b-2-a-1-2-1-b-2-a-b-2-2-1-4-a-b-3-a-1-3-1-b-3-a-b-3-

Question Number 142325 by loveineq last updated on 30/May/21 $$\mathrm{Given}\:\mathrm{that}\:{a}\:\geqslant\:\mathrm{1}\:\geqslant\:{b}\:>\:\mathrm{0}.\:\mathrm{Prove}\:\mathrm{the}\:\mathrm{followings}:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\left(\mathrm{1}\right)\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{\mathrm{1}}{\mathrm{2}}\left({a}−{b}\right)^{\mathrm{2}} \:\leqslant\:\left({a}−\mathrm{1}\right)^{\mathrm{2}} +\left(\mathrm{1}−{b}\right)^{\mathrm{2}} \:\leqslant\:\left({a}−{b}\right)^{\mathrm{2}} \:\:\:\: \\ $$$$\left(\mathrm{2}\right)\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{\mathrm{1}}{\mathrm{4}}\left({a}−{b}\right)^{\mathrm{3}} \:\leqslant\:\left({a}−\mathrm{1}\right)^{\mathrm{3}} +\left(\mathrm{1}−{b}\right)^{\mathrm{3}} \:\leqslant\:\left({a}−{b}\right)^{\mathrm{3}} \\ $$$$ \\ $$…

x-0-2pi-2cos-2-x-sinx-1-0-x-

Question Number 11249 by uni last updated on 18/Mar/17 $${x}\in\left(\mathrm{0},\mathrm{2}\pi\right) \\ $$$$\mathrm{2cos}^{\mathrm{2}} {x}\:+{sinx}−\mathrm{1}=\mathrm{0}\:\Rightarrow\Sigma{x}=?\: \\ $$ Answered by ajfour last updated on 18/Mar/17 $$\mathrm{2}−\mathrm{2sin}\:^{\mathrm{2}} \mathrm{x}+\mathrm{sin}\:\mathrm{x}−\mathrm{1}=\mathrm{0} \\…

cos10-cos20-cos40-

Question Number 11245 by uni last updated on 18/Mar/17 $${cos}\mathrm{10}×{cos}\mathrm{20}×{cos}\mathrm{40}=? \\ $$ Answered by b.e.h.i.8.3.4.1.7@gmail.com last updated on 18/Mar/17 $$\frac{\mathrm{2}{sin}\mathrm{10}.{cos}\mathrm{10}.{cos}\mathrm{20}.{cos}\mathrm{40}}{\mathrm{2}{sin}\mathrm{10}}= \\ $$$$\frac{{sin}\mathrm{20}.{cos}\mathrm{20}.{cos}\mathrm{40}}{\mathrm{2}{sin}\mathrm{10}}=\frac{\frac{\mathrm{1}}{\mathrm{2}}{sin}\mathrm{40}.{cos}\mathrm{40}}{\mathrm{2}{sin}\mathrm{10}}= \\ $$$$\frac{\frac{\mathrm{1}}{\mathrm{4}}{sin}\mathrm{80}}{\mathrm{2}{sin}\mathrm{10}}=\frac{\mathrm{1}}{\mathrm{8}}.\frac{{cos}\mathrm{10}}{{sin}\mathrm{10}}=\frac{\mathrm{1}}{\mathrm{8}}\mathrm{cot}\:\mathrm{10}\:\:\blacksquare \\…

prove-that-cos-40-1-3-cos-80-1-3-cos-20-1-3-3-2-9-1-3-2-1-3-

Question Number 76777 by aliesam last updated on 30/Dec/19 $${prove}\:{that} \\ $$$$ \\ $$$$\sqrt[{\mathrm{3}}]{{cos}\left(\mathrm{40}°\right)}\:+\:\sqrt[{\mathrm{3}}]{{cos}\left(\mathrm{80}°\right)}\:−\:\sqrt[{\mathrm{3}}]{{cos}\left(\mathrm{20}°\right)}\:=\sqrt[{\mathrm{3}}]{\frac{\mathrm{3}}{\mathrm{2}}\left(\sqrt[{\mathrm{3}}]{\mathrm{9}}−\mathrm{2}\right)} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com