Determine whether each of the statements that follow are TRUE or FALSE. Circle y

Question

Determine whether each of the statements that follow are TRUE or FALSE. Circle your selection. If a statement is false, give a counterexample (state an {an} and/or {&} that contradict the statement) Every increasing sequence of negative number is convergent. If the tail of a sequence converge, then the entire sequence converges. If {an} and {fcn} both diverge, then {an + bn} diverges. If an is lesserthan or equal to bn is lesserthan or equal to cn and {an} & {bn} converge, then {bn} converges. If an = f(n) for n =1,2,3,. . . , then f(x) = an.

Explanation / Answer

1) T Because if the negative number increases then finally it will tend to zero hence, it will converge.

2) T when the tail converges then value tends to some certain value. Therefore the value converges.

3) F bn can be exactly opposite to an hence they will cancel each other and series will converge.

4) T question is alredy saying that bn converges.

5) F as the given function is only defined for positive integer.

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