(a) If Xn=1-1/2+1/3-...-1/(2n), show that Xn -> log 2 as n -> oo, by using the definition of Euler's constant. Hint: Show that Xn=C2n-Cn + log2 in the notation

(b) Prove that the partial sums of the series

1+1/2-1/3+1/4+1/5-1/6++- ...

approach + oo as n -> oo. Make use of Euler's constant

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