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Exercises1 - n ∀ ∈ Z Show that n n=1 a ∞ ∑...

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Exercises – 1 1) Find sum of the series 1 1 1 1 1 1 2 1 2 3 1 2 3 4 + + + + + + + + + + 2) If the n th partial sum of a series 1 n n a = is 1 1 n s n = + ; a) find n a . b) determine whether the series converges. 3) Show that 1 1 ln(1 ) n n = + diverges. 4) Suppose that n n=1 a has positive terms (i.e. a n > 0 n + ∀ ∈ Zbb ) and its partial sums s n satisfy s n K for some K>0,
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Unformatted text preview: n + ∀ ∈ Z . Show that n n=1 a ∞ ∑ converges. 5) Find b if 1+e b +e 2b +e 3b + . .. = 9 6) Write 1,24123 as the ratio of two integers. 7) Determine whether the sequence 1/ ( 4) {( 4) } n n + + is convergent or divergent. If it is convergent find its limit....
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