Let `S_(n)=1+2+3+...+n " and " P_(n)=(S_(2))/(S_(2)-1).(S_(3))/(S_(3)-1).(S_(4))/(S_(4)-1)...(S_(n))/(S_(n)-1)`, where `n inN,(nge2) Then ``underset(ntooo)limP_(n)`=__________.A. `(1)/(4)`B. `(1)/(24)`C. `(1)/(16)`D. `(1)/(8)`

Let `S_(n)=1+2+3+...+n " and " P_(n)=(S_(2))/(S_(2)-1).(S_(3))/(S_(3)-

1.	Let `S_(n)=1+2+3+...+n " and " P_(n)=(S_(2))/(S_(2)-1).(S_(3))/(S_(3)-1).(S_(4))/(S_(4)-1)...(S_(n))/(S_(n)-1)`, where `n inN,(nge2) Then ``underset(ntooo)limP_(n)`=__________.A. `(1)/(4)`B. `(1)/(24)`C. `(1)/(16)`D. `(1)/(8)`
Answer» Correct Answer - `(3)` `S_(n)=(n(n+1))/(n)" and "S_(n)-1=((n+2)(n-1))/(2)` `:." "(S_(n))/(S_(n)-1)=(n(n+1))/(2).(2)/((n+2)(n-1))=((n)/(n-1))((n+1)/(n+2))` `:." "P_(n)=((2)/(1).(3)/(2).(4)/(3).(5)/(4)...(n)/(n-1))((3)/(4).(4)/(5).(5)/(6)...(n+1)/(n+2))` `=((n)/(1))((3)/(n+2))` `:." "underset(ntooo)limP_(n)=3`

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