数列求和.已知an=(0.5)^n,设bn/an=(2n+5)/((2n+1)(2n+3)),求bn的前n项和.
数列求和.已知an=(0.5)^n,设bn/an=(2n+5)/((2n+1)(2n+3)),求bn的前n项和.
数学人气:864 ℃时间:2020-01-29 14:05:42
优质解答
bn/an = (2n+5)/[(2n+1)(2n+3)]= 2/(2n+1) - 1/(2n+3)bn =[2/(2n+1) - 1/(2n+3)] (0.5)^nSn = b1+b2+..+bn= [( 1/3 -1/10)+ (1/10-1/28)+(1/28-1/72)+.( 2/(2n+1)(0.5)^n - 1/[2^n(2n+3)]) ]= 1/3 - 1/[2^n(2n+3)]
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