(n+1) sint dt. -T- Consider the infinite series S = > u, where u, = (a)...

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(n+1) sint dt. -T- Consider the infinite series S = > u, where u, = (a) Explain why the series is alternating. (b) ) Use the substitution 7 =t-x in the expression for u, to show that lu, 1l < lu,1. (ii) Show that the series is convergent. [1] [9] (c) Show that S < 1.65. [4] (n+1) sint dt. -T- Consider the infinite series S = > u, where u, = (a) Explain why the series is alternating. (b) ) Use the substitution 7 =t-x in the expression for u, to show that lu, 1l < lu,1. (ii) Show that the series is convergent. [1] [9] (c) Show that S < 1.65. [4]