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1) if a sequence is monotone decreasing and greater than 0 for all values of n...

1) if a sequence is monotone decreasing and greater than 0 for all values of n (n=1 to infinity) then the sequence must converge. True or false?

2) In order for infinite series k=1 to infinity (ak + bk) = series ak + series bk, both series must converge. True or false?

3) Let f(x) be a continuous decreasing function where f(k) = ak. If integral 1 to infinity f(x) = 5, what can we conclude about series ak?

-series must converge

-must diverge

- must converge to 5

- no conclusion can be made

Math   Calculus   
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