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Category: Algebra

1-2-3-4-1-3-4-5-1-4-5-6-1-5-6-7-1-6-7-8-1-12-13-14-

Question Number 148838 by liberty last updated on 31/Jul/21 $$\:\frac{\mathrm{1}}{\mathrm{2}×\mathrm{3}×\mathrm{4}}\:+\frac{\mathrm{1}}{\mathrm{3}×\mathrm{4}×\mathrm{5}}+\frac{\mathrm{1}}{\mathrm{4}×\mathrm{5}×\mathrm{6}}+\frac{\mathrm{1}}{\mathrm{5}×\mathrm{6}×\mathrm{7}}+\frac{\mathrm{1}}{\mathrm{6}×\mathrm{7}×\mathrm{8}}+…+\frac{\mathrm{1}}{\mathrm{12}×\mathrm{13}×\mathrm{14}}=? \\ $$ Commented by JDamian last updated on 31/Jul/21 $${Can}\:{you}\:{confirm}\:{there}\:{is}\:{a}\:{missing}\:\frac{\mathrm{1}}{\mathrm{4}×\mathrm{5}×\mathrm{6}}? \\ $$ Commented by liberty…

Question-83262

Question Number 83262 by peter frank last updated on 29/Feb/20 Answered by mr W last updated on 29/Feb/20 $${curve}\:\mathrm{1}:\:{x}^{\mathrm{2}} +\mathrm{4}{y}^{\mathrm{2}} =\mathrm{8}\:\:\:…\left({i}\right) \\ $$$${curve}\:\mathrm{2}:\:{x}^{\mathrm{2}} −\mathrm{2}{y}^{\mathrm{2}} =\mathrm{4}\:\:\:…\left({ii}\right)…

Evaluate-3-2-

Question Number 17713 by tawa tawa last updated on 09/Jul/17 $$\mathrm{Evaluate}:\:\:\:\:\left(−\sqrt{\mathrm{3}}\right)^{\left(−\sqrt{\mathrm{2}}\right)} \\ $$ Commented by b.e.h.i.8.3.417@gmail.com last updated on 09/Jul/17 $${a}=\left(−\sqrt{\mathrm{3}}\right)^{\left(−\sqrt{\mathrm{2}}\right)} \\ $$$${lna}=−\sqrt{\mathrm{2}}{ln}\left(−\sqrt{\mathrm{3}}\right)=−\sqrt{\mathrm{2}}{ln}\left({i}^{\mathrm{2}} \sqrt{\mathrm{3}}\right)= \\…

Question-148776

Question Number 148776 by liberty last updated on 31/Jul/21 Answered by mathmax by abdo last updated on 31/Jul/21 $$\mathrm{P}=\prod_{\mathrm{k}=\mathrm{2}} ^{\mathrm{2020}} \:\frac{\mathrm{k}^{\mathrm{2}} }{\mathrm{k}^{\mathrm{2}} −\mathrm{1}}=\prod_{\mathrm{k}=\mathrm{2}} ^{\mathrm{2020}} \:\frac{\mathrm{k}}{\mathrm{k}−\mathrm{1}}×\frac{\mathrm{k}}{\mathrm{k}+\mathrm{1}}…