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Using Mathematical Induction , prove tha...

Using Mathematical Induction , prove that statement for all `n inN`
`(1+(3)/(1))(1+(5)/(4))(1+(7)/(9)).......(1+(2n+1)/(n^(2)))=(n+1)^(2)`

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Lt_(x to oo)((1)/(3.5)+(1)/(5.7)+.....+(1)/((2n+1)(2n+3)))=

underset(n to oo)lim {(1)/(1.3)+(1)/(3.5)+(1)/(5.7)+.....+(1)/((2n-1)(2n+1))}=

Lt_(n to oo) ((1)/(1.5)+(1)/(5.9)+....+(1)/((4n-3)(4n+1)))=