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Question Number 57251 by ANTARES VY last updated on 01/Apr/19

Answered by tanmay.chaudhury50@gmail.com last updated on 01/Apr/19

$$T_n=\frac{n(n-1)}{\frac{1}{(n-1)!}+\frac{1}{(n-2)!}}$$$$=\frac{n(n-1)}{\frac{1+n-1}{(n-1)!}}\to (n-1)(n-1)!$$$$[\underset{n=3}{\sum ^{2019}}(n-1)(n-1)!]+2\to \mathit{S}+2$$$$$$$$T_3=\left(2\right)\times 2!$$$$T_4=\left(3\right)\times 3!$$$$T_5=\left(4\right)\times 4!$$$$...$$$$...$$$$T_{2019}=\left(2018\right)\times \left(2018\right)!$$$$sorequiredsumtotal=$$$$2+\underset{n=3}{\sum ^{2019}}(n-1)(n-1)!$$$$othersplscheck...$$

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