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lim(n->oo) {1/1.3+1/3.5+1/5.7+.....+1/((...

`lim_(n->oo) {1/1.3+1/3.5+1/5.7+.....+1/((2n+1)(2n+3))` is equal to

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`lim_(n->oo)[1/2((3-1)/(1.3))+1/2((5-3)/(3.5))+...+1/2(((2n+3)-(2n+1))/((2n+1)(2n+3)))]`
`lim_(h->oo)[1/2(1-1/3_+(1/3-1/5)+(1/5-1/7)+...+(1/(2n+1)-1/(2n+3))]`
`lim_(h->oo)1/2(1-1/(2n+3))`
`lim_(h->oo)1/2((2n+2)/(2n+3))`
`lim_(h->oo)1/2((2n(1+1/n))/(h(2+3/n)))`
`1/2(2(1+0))/(2+0)`
`1/2`.
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