(a) Find the Maclaurin series for ln(1+x). (b) Use the alternating series estimation theorem to prove that x-- -ln(1+x) x. (c) Hence or otherwise prove that 2 x 1 In(n + 1) Inn < . (d) Using your result in (c) show that 1++...+ -> ln(n+1). 2 n n (e) Hence deduce that the harmonic series 1 1 k diverges.