设f(x)在区间[a,b]上满足a≤f(x)≤b,且有|f’(x)|≤q<1,令μn=f(μn-1)(n=1,2,…),μ0∈[a,b],证明:级数(μn+1一μn)绝对收敛.

admin2017-08-31  28

问题 设f(x)在区间[a,b]上满足a≤f(x)≤b,且有|f(x)|≤q<1,令μn=f(μn-1)(n=1,2,…),μ0∈[a,b],证明:级数n+1一μn)绝对收敛.

选项

答案由|μn+1一μn|=|f(μn)一f(μn-1)|=|f1)||μn一μn-1|≤q|μn一μn-1|≤q2|μn-1-μn-2|≤…≤qn|μ1一μ0| [*]

解析
转载请注明原文地址:https://kaotiyun.com/show/ELr4777K
0

最新回复(0)