Quote:
Originally Posted by rb30999 Posting for the first time on pg and a problem straightaway
Hall and knight chapter on geometric progression, exercise no. V.b. ques 21 and 23
21. If Sn denotes the sum of a GP whose first term is a and common ratio r, find the sum of S1, S2, S3......S(2n-1). (I hope it is understood here that S(2n-1) means sum of 2n-1 terms)
23. If r<1 and and positive and m is a positive integer, show that
(2m+1)r^m * (1-r) < (1-r)^(2m+1)
I would really appreciate it if anyone could plz give me a detailed solution with each step explained |
we know that S(k)=k[2a+(k-1)r]/2
now we have to sume S(k) for k=1 to 2n-1
S= a.(2n-1).2n/2+ r[ 2n.(2n-1)(4n+1)/6 -2n.(2n-1)/2]/2
=n.(2n-1)[a -r/2] +r.n.(2n-1).(4n+1)/6
we can further solve it if the options so demand