72 72 (14 marks) Denote (1+ binomial expansion (when expressed in ascending powers of ), and n € N. 6.)" =Ź Fme, where F

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72 72 14 Marks Denote 1 Binomial Expansion When Expressed In Ascending Powers Of And N N 6 Z Fme Where F 1 (35.19 KiB) Viewed 44 times

72 72 (14 marks) Denote (1+ binomial expansion (when expressed in ascending powers of ), and n € N. 6.)" =Ź Fme, where Fox is the (x + 1) th term of its ke=0 72 (a) Show that Σ Frk < 3 for all n EN ke=0 (b) Fix the value of k to show that the limit of the sequence {F},4, Fx+1,4, F#+2,4, Fx+3,4,} exists. 72 (c) (i) Let k > 1. Use calculus to show that (1+x)* - 1 > kx for every x > 0. (ii) Using (i), show that Fm,k is strictly increasing for all n E N. (Note: NO marks will be given if you do not use the result of (c) (i).) ku