Tính nhanh tổng sau : 1-3+5-7+9-11+13-15+17-19+……+97-99+101 04/11/2021 Bởi Eden Tính nhanh tổng sau : 1-3+5-7+9-11+13-15+17-19+……+97-99+101
`1-3+5-7+9-11+13-15+17-19+……+97-99+101` `= (1-3)+(5-7)+(9-11)+(13-15)+(17-19)+……+(97-99)+101` $= \underbrace{(-2)+(-2)+(-2)+(-2)+(-2)+…+(-2)}_{25\quad số \quad hạng\quad (-2)}+101$ `= (-2).25+101` `= -50+101` `= 51` Bình luận
`1 -3 + 5 – 7 + 9 – 11 + 13 – 15 + 17 – 19 + … + 97 – 99 + 101` `= 1 + ( -3 ) + 5 + ( -7 ) + 9 + ( -11 ) + 13 + ( -15) + 17 + (-19) + … + 97 + ( -99 ) + 101` `= ( 1 + 5 + 9 + 13 + 17 + … + 101 ) + [ -3 + ( -7 ) + ( -11 ) + ( -15 ) + ( -19 ) + … + (-99 ) ]` `= \frac{(1+101)[(|101|-|1|) : 4 + 1]}{2} + \frac{[(-99) + (-3)[(|-99| – |-3|):4 + 1]{2}` `= 1326 + (-1275)` `=51` Bình luận
`1-3+5-7+9-11+13-15+17-19+……+97-99+101`
`= (1-3)+(5-7)+(9-11)+(13-15)+(17-19)+……+(97-99)+101`
$= \underbrace{(-2)+(-2)+(-2)+(-2)+(-2)+…+(-2)}_{25\quad số \quad hạng\quad (-2)}+101$
`= (-2).25+101`
`= -50+101`
`= 51`
`1 -3 + 5 – 7 + 9 – 11 + 13 – 15 + 17 – 19 + … + 97 – 99 + 101`
`= 1 + ( -3 ) + 5 + ( -7 ) + 9 + ( -11 ) + 13 + ( -15) + 17 + (-19) + … + 97 + ( -99 ) + 101`
`= ( 1 + 5 + 9 + 13 + 17 + … + 101 ) + [ -3 + ( -7 ) + ( -11 ) + ( -15 ) + ( -19 ) + … + (-99 ) ]`
`= \frac{(1+101)[(|101|-|1|) : 4 + 1]}{2} + \frac{[(-99) + (-3)[(|-99| – |-3|):4 + 1]{2}`
`= 1326 + (-1275)`
`=51`