Determine whether the following statements are true and give an explanation or counterexample.

a. If

b. If

c. The convergent sequences {a_n} and {b_n} differ in their first 100 terms, but a_n = b_n, for n > 100. It follows that

d. If

e. If the sequence {a_n} converges, then the sequence {(-1)ⁿ a_n} converges.

f. If the sequence {a_n} diverges, then the sequence {0.000001 a_n} diverges.

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lim an ∞07U = 1 and lim bn 007U b₁ n = 3, then lim = 3. n→∞ An lim_ añ = 0 and lim bn n→∞ n→∞ || ∞, then lim an bn = 0. n→∞ lim an n→∞ = lim bn. n→∞ {an} = 1 1 1 1 { 1, 2, 3, 4, 5, .} and {bn} = {1,0, ½, 0, ½, 0, 1, 0, . . . }, then lim a„ = lim b„. n→∞ n→∞