Đáp án:
Giải thích các bước giải:
Đặt:`S=1/1.3 + 1/3.5 + ... + 1/199.201`
`=>2S=2/1.3 + 2/3.5 + ... + 2/199.201`
`=>2S=1-1/3+1/3-1/5+....+1/199-1/201`
`=>2S=1-1/201`
`=>2S=200/201`
`=>S=200/201:2=100/201`
`1/(1*3) + 1/(3*5) + ... + 1/(199*201)`
`= 1/2*(1-1/3+1/3-1/5+...+1/199-1/201)`
`=1/2*(1-1/201)`
`=1/2*(201/201-1/201)`
`=1/2*200/201`
`=200/402`
`=100/201`
#letienlong682008
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