tính (1+1/2) .(1+1/3).(1+1/4)..(1+1/100) 28/07/2021 Bởi Caroline tính (1+1/2) .(1+1/3).(1+1/4)..(1+1/100)
Đáp án: Giải thích các bước giải: $\left (1+\dfrac{1}{2} \right )\left (1+\dfrac{1}{3} \right )\left (1+\dfrac{1}{4} \right )….\left (1+\dfrac{1}{100} \right )$ $=\left (\dfrac{2}{2}+\dfrac{1}{2} \right )\left (\dfrac{3}{3}+\dfrac{1}{3} \right )\left (\dfrac{4}{4}+\dfrac{1}{4} \right )….\left (\dfrac{100}{100}+\dfrac{1}{100} \right )$ $=\dfrac{3}{2}.\dfrac{4}{3}.\dfrac{5}{4}….\dfrac{101}{100}$ $=\dfrac{1}{2}.101$ $=\dfrac{101}{2}=50,5$ Bình luận
`(1+1/2).(1+1/3).(1+1/4)…….(1+1/100)` `=3/2.4/3.5/4…….101/100` ` =(3.4.5……101)/(2.3……100)` `=101/2` Bình luận
Đáp án:
Giải thích các bước giải:
$\left (1+\dfrac{1}{2} \right )\left (1+\dfrac{1}{3} \right )\left (1+\dfrac{1}{4} \right )….\left (1+\dfrac{1}{100} \right )$
$=\left (\dfrac{2}{2}+\dfrac{1}{2} \right )\left (\dfrac{3}{3}+\dfrac{1}{3} \right )\left (\dfrac{4}{4}+\dfrac{1}{4} \right )….\left (\dfrac{100}{100}+\dfrac{1}{100} \right )$
$=\dfrac{3}{2}.\dfrac{4}{3}.\dfrac{5}{4}….\dfrac{101}{100}$
$=\dfrac{1}{2}.101$
$=\dfrac{101}{2}=50,5$
`(1+1/2).(1+1/3).(1+1/4)…….(1+1/100)`
`=3/2.4/3.5/4…….101/100`
` =(3.4.5……101)/(2.3……100)`
`=101/2`