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Find the value of prod(n=2)^(n) (1 - (1...

Find the value of `prod_(n=2)^(n) (1 - (1)/(n^(2)))`

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`t_(n) = 1 - (1)/(n^(2)) = (n^(2) -1)/(n^(2) ) = ((n-1)(n+1))/(n^(2) ) = (n-1)/(n) (n+1)/(n)`
Putting n = 2, 3,…, n is succession
`t_(2) = (1)/(2).(3)/(2)`
`t_(3)= (2)/(3).(4)/(3)`
`t_(4) = (3)/(4).(5)/(4)`
......
`t_(n) = (n-1)/(n) = (n+1)/(2n) = (1)/(2) (1 + (1)/(n))1`
Upon multiplying , we get
`t_(2) t_(3)t_(4) ...t_(n) = ((1)/(2). (3)/(2)) ((2)/(3) .(5)/(4)) ((3)/(4).(5)/(4)) ...((n-1)/(n) .(n+1)/(n))`
`= (1)/(2) (n+1)/(2n) = (1)/(2) (1 + (1)/(n))`
`prod_(2)^(n) (1 -(1)/(n^(2))) = (1)/(2) (1 +(1)/(n))`
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