The method lim() does not return a simple integer

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Hi,

I have two cases where I would expect the answer to be a simple integer when I take the limit using lim(..)

lim(i/(i+1),i=infinity)

This answer should be 1. Instead I get: 1/2*I + 1/2

lim(1/((2i+3)(2*i+2)),i=+oo)

Similarly, the answer should be 0

Instead I get this form:

-5/52*I + 1/52

Question: Am I using the right method, od do I need to add more constraints ?

thanks Pat