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if-the-point-A-B-C-with-position-vector-20i-j-5i-j-and-10i-13j-are-collinear-then-the-value-of-is-

Question Number 62241 by vishnurajput8081@gmail.com last updated on 18/Jun/19 $$\boldsymbol{{if}}\:\boldsymbol{{the}}\:\boldsymbol{{point}}\:{A}\:{B}\:{C}\:{with}\:{position}\:{vector}\: \\ $$$$\left(\mathrm{20}\hat {{i}}+\lambda\hat {{j}}\right)\:\left(\mathrm{5}\hat {{i}}−\hat {{j}}\right)\:{and}\left(\mathrm{10}\hat {{i}}−\mathrm{13}\hat {{j}}\right)\:{are} \\ $$$${collinear}\:{then}\:{the}\:{value}\:{of}\:\lambda\:{is}: \\ $$ Answered by tanmay…

1-1-pi-2-1-pi-2-2pi-2-2-pi-2-3pi-2-3-pi-2-4pi-2-4-pi-2-5pi-2-5-pi-2-

Question Number 127771 by Dwaipayan Shikari last updated on 01/Jan/21 $$\frac{\mathrm{1}}{\mathrm{1}−\frac{\pi^{\mathrm{2}} }{\mathrm{1}+\pi^{\mathrm{2}} −\frac{\mathrm{2}\pi^{\mathrm{2}} }{\mathrm{2}+\pi^{\mathrm{2}} −\frac{\mathrm{3}\pi^{\mathrm{2}} }{\mathrm{3}+\pi^{\mathrm{2}} −\frac{\mathrm{4}\pi^{\mathrm{2}} }{\mathrm{4}+\pi^{\mathrm{2}} −\frac{\mathrm{5}\pi^{\mathrm{2}} }{\mathrm{5}+\pi^{\mathrm{2}} ….}}}}}} \\ $$ Commented by…

pi-2-1-pi-2-3-pi-2-9pi-2-5-3pi-2-25pi-2-7-5pi-2-49pi-2-9-7pi-2-81pi-2-11-9pi-2-121pi-2-

Question Number 127682 by Dwaipayan Shikari last updated on 31/Dec/20 $$\frac{\pi^{\mathrm{2}} }{\mathrm{1}+\frac{\pi^{\mathrm{2}} }{\mathrm{3}−\pi^{\mathrm{2}} +\frac{\mathrm{9}\pi^{\mathrm{2}} }{\mathrm{5}−\mathrm{3}\pi^{\mathrm{2}} +\frac{\mathrm{25}\pi^{\mathrm{2}} }{\mathrm{7}−\mathrm{5}\pi^{\mathrm{2}} +\frac{\mathrm{49}\pi^{\:\mathrm{2}} }{\mathrm{9}−\mathrm{7}\pi^{\mathrm{2}} +\frac{\mathrm{81}\pi^{\mathrm{2}} }{\mathrm{11}−\mathrm{9}\pi^{\mathrm{2}} +\frac{\mathrm{121}\pi^{\mathrm{2}} }{…..}}}}}}} \\ $$…

1-1-1-2-1-2-3-2-1-3-4-3-1-4-5-4-1-5-6-5-

Question Number 127644 by Dwaipayan Shikari last updated on 31/Dec/20 $$\frac{\mathrm{1}}{\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}−\frac{\frac{\mathrm{1}}{\mathrm{2}}}{\frac{\mathrm{3}}{\mathrm{2}}−\frac{\frac{\mathrm{1}}{\mathrm{3}}}{\frac{\mathrm{4}}{\mathrm{3}}−\frac{\frac{\mathrm{1}}{\mathrm{4}}}{\frac{\mathrm{5}}{\mathrm{4}}−\frac{\frac{\mathrm{1}}{\mathrm{5}}}{\frac{\mathrm{6}}{\mathrm{5}}−…}}}}}} \\ $$ Commented by Dwaipayan Shikari last updated on 31/Dec/20 $${a}_{\mathrm{0}} +{a}_{\mathrm{0}} {a}_{\mathrm{1}} +{a}_{\mathrm{0}}…

Correct-me-if-I-am-wrong-1-1-3-x-1-y-1-i-1-

Question Number 62036 by Cypher1207 last updated on 14/Jun/19 $$\mathrm{Correct}\:\mathrm{me}\:\mathrm{if}\:\mathrm{I}\:\mathrm{am}\:\mathrm{wrong}. \\ $$$$\underset{\:\sqrt{−\mathrm{1}}=\mathrm{1}} {\overset{\mathrm{3}} {\sum}}\mathrm{x}_{\sqrt{−\mathrm{1}}} +\mathrm{y}_{\sqrt{−\mathrm{1}}} \\ $$$$\therefore\left({i}=\sqrt{−\mathrm{1}}\right) \\ $$$$ \\ $$ Commented by Rasheed.Sindhi last…