is a sequence of real numbers satisfying then
If x1 = 4 and then the sequence {xn} converge to
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Let (an) be an increasing sequence of positive real numbers such that the series is divergent. Let for n = 2, 3, .... Then tn is equal to
Which of the following series is divergent?
Let ∑un be a series of positive terms such that Then,
(i) if l > 1, the series converges;
(ii) if l < 1, the series diverges;
(iii) if l = 1, the series may either converge or diverge and therefore the test fails;
This theorem is known as
The set of all x at which the power series converges is
If {xn} is a sequence of real numbers, then match list I with list II and select the correct answer using codes given below the lists
List I (sequences)
List II (limit of sequences)
∑un is a series of positive terms. If Sn = u1 + n2 + ... + un, then
Which amongst the following expressions is not true?
where an > 0 n, then (a1 a2 a3...an)1/n = l. Above theorem is known as
Which amongst the following expresses the Cauchy’s first theorem on limits?