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19-20-21-factorial-plz-hepl-me-so-soon-

Question Number 196347 by bbbbbbbb last updated on 23/Aug/23 $$\left(\mathrm{1}\overset{\left(\mathrm{2}\overset{\mathrm{21}} {\mathrm{0}}\right)} {\mathrm{9}}\right)\:\boldsymbol{\mathrm{factorial}}\:\boldsymbol{\mathrm{plz}}\:\boldsymbol{\mathrm{hepl}}\:\boldsymbol{\mathrm{me}}\:\boldsymbol{\mathrm{so}}\:\boldsymbol{\mathrm{soon}} \\ $$ Commented by mr W last updated on 23/Aug/23 $${so}\:{soon}\:{as}\:{the}\:{light}? \\ $$$${in}\:{each}\:{of}\:{your}\:{questions}\:{you}\:{request}…

Question-196303

Question Number 196303 by sonukgindia last updated on 22/Aug/23 Answered by sniper237 last updated on 22/Aug/23 $$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\:{Im}\left(\frac{{e}^{{i}\pi/\mathrm{4}} }{\mathrm{2}}\right)^{{n}} ={Im}\left(\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left({e}^{{i}\pi/\mathrm{4}} /\mathrm{2}\right)^{{n}} \right)…

Question-196324

Question Number 196324 by sonukgindia last updated on 22/Aug/23 Answered by sniper237 last updated on 22/Aug/23 $${a}\left(\mathrm{22}\right)−{a}\left(\mathrm{21}\right)=\mathrm{3}×\mathrm{21}−\mathrm{1} \\ $$$${a}\left(\mathrm{21}\right)−{a}\left(\mathrm{20}\right)=\mathrm{3}×\mathrm{20}−\mathrm{1} \\ $$$$… \\ $$$${a}\left(\mathrm{3}\right)−{a}\left(\mathrm{2}\right)=\mathrm{3}×\mathrm{2}−\mathrm{1} \\ $$$${a}\left(\mathrm{2}\right)−{a}\left(\mathrm{1}\right)=\mathrm{3}×\mathrm{1}−\mathrm{1}…