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Let Sn=1+2+3++n and Pn=(S2)/(S2-1)dot(S...

Let `S_n=1+2+3++n` and `P_n=(S_2)/(S_2-1)dot(S_3)/(S_3-1)dot(S_4)/(S_4-1)...(S_n)/(S_n-1)` Where `n in N ,(ngeq2)dot` Then `("lim")_(n→oo)P_n=______`

A

`(1)/(4)`

B

`(1)/(24)`

C

3

D

`(1)/(8)`

Text Solution

Verified by Experts

The correct Answer is:
`(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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