*4*

*Series and limits*

**4.1***Sum the even numbers between* 1000 *and* 2000 *inclusive.*

We must first express the given sum in terms of a summation for which we have an explicit form. The result that is needed is clearly

and we must re-write the given summation in terms of sums of this form:

**4.3***How does the convergence of the series*

*depend on the integer ...*

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