Quod Erat Demonstrandum

2012/01/07

某題-級數

Filed under: Fun,HKALE,Pure Mathematics — johnmayhk @ 12:04 上午

以下是數列 {a_n}

1 , 12 , 123 , 1234 , … , 12345678910 , 1234567891011 , …

以下是數列 {b_n}(把 a_n「倒寫」)

1 , 21 , 321 , 4321 , … , 10987654321 , 1110987654321 , …

以下是數列 {\frac{a_n}{b_n}},即

1,\frac{12}{21},\frac{123}{321},\frac{1234}{4321},\dots

問:把上述數列求和,即

1+\frac{12}{21}+\frac{123}{321}+\frac{1234}{4321}+\dots

是否收歛?

答案

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