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Unformatted text preview: 1. This question should be very easy once you’ve done part b.) 3. Consider the series ∞ X n =1 1 n ( n + 1) (a) Expand the expression 1 n ( n + 1) using partial fractions and deduce a pattern for the n th partial sum s n . (HINT: Once expanded, compute a few partial sums s 1 ,s 2 ,s 3 etc. Leave each expression semisimpliﬁed, i.e. do not ﬁnd a common denominator) (b) Compute the value of ∞ X n =1 1 n ( n + 1) (c) Find the sum of the series 1 + 1 1 + 2 + 1 1 + 2 + 3 + 1 1 + 2 + 3 + 4 + ··· 4. Show that the series ∞ X n =1 ln ± 1 + 1 n ² passes the divergence test yet fails to converge. 2...
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 Fall '07
 Anoymous
 Math, Calculus, Summation, partial sum sn

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