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Obtain-the-general-term-of-each-of-the-following-sequences-if-obtainable-in-terms-of-or-any-other-form-of-notation-A-1-1-n-1-2n-1-n-1-2n-1-3n-1-4n-1-n-1-2n-1-3n-1-4n-1-5n-1




Question Number 1105 by Yugi last updated on 14/Jun/15
Obtain the general term of each of the following sequences (if obtainable)  in terms of Π (or any other form of notation):  A)   1,(1−n)(1−2n) , (1−n)(1−2n)(1−3n)(1−4n) , (1−n)(1−2n)(1−3n)(1−4n)(1−5n)(1−6n), ...  B)   1, 1−n , (1−n)(1−2n)(1−3n) , (1−n)(1−2n)(1−3n)(1−4n)(1−5n), ...
$${Obtain}\:{the}\:{general}\:{term}\:{of}\:{each}\:{of}\:{the}\:{following}\:{sequences}\:\left({if}\:{obtainable}\right) \\ $$$${in}\:{terms}\:{of}\:\Pi\:\left({or}\:{any}\:{other}\:{form}\:{of}\:{notation}\right): \\ $$$$\left.{A}\right)\:\:\:\mathrm{1},\left(\mathrm{1}−{n}\right)\left(\mathrm{1}−\mathrm{2}{n}\right)\:,\:\left(\mathrm{1}−{n}\right)\left(\mathrm{1}−\mathrm{2}{n}\right)\left(\mathrm{1}−\mathrm{3}{n}\right)\left(\mathrm{1}−\mathrm{4}{n}\right)\:,\:\left(\mathrm{1}−{n}\right)\left(\mathrm{1}−\mathrm{2}{n}\right)\left(\mathrm{1}−\mathrm{3}{n}\right)\left(\mathrm{1}−\mathrm{4}{n}\right)\left(\mathrm{1}−\mathrm{5}{n}\right)\left(\mathrm{1}−\mathrm{6}{n}\right),\:… \\ $$$$\left.{B}\right)\:\:\:\mathrm{1},\:\mathrm{1}−{n}\:,\:\left(\mathrm{1}−{n}\right)\left(\mathrm{1}−\mathrm{2}{n}\right)\left(\mathrm{1}−\mathrm{3}{n}\right)\:,\:\left(\mathrm{1}−{n}\right)\left(\mathrm{1}−\mathrm{2}{n}\right)\left(\mathrm{1}−\mathrm{3}{n}\right)\left(\mathrm{1}−\mathrm{4}{n}\right)\left(\mathrm{1}−\mathrm{5}{n}\right),\:… \\ $$
Commented by prakash jain last updated on 14/Jun/15
Question is not very clear.  The general term can be defined in  terms of Π notation, but I don′t think that is  what you are looking for.
$$\mathrm{Question}\:\mathrm{is}\:\mathrm{not}\:\mathrm{very}\:\mathrm{clear}. \\ $$$$\mathrm{The}\:\mathrm{general}\:\mathrm{term}\:\mathrm{can}\:\mathrm{be}\:\mathrm{defined}\:\mathrm{in} \\ $$$$\mathrm{terms}\:\mathrm{of}\:\Pi\:\mathrm{notation},\:\mathrm{but}\:\mathrm{I}\:\mathrm{don}'\mathrm{t}\:\mathrm{think}\:\mathrm{that}\:\mathrm{is} \\ $$$$\mathrm{what}\:\mathrm{you}\:\mathrm{are}\:\mathrm{looking}\:\mathrm{for}. \\ $$

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