Question

100≤x≤101 ,Expresia E(x)=|1-x|+|2-x|+...+|200-x| este......

Answer 1

100≤x≤101

E(x)=|1-x|+|2-x|+...+|200-x|

x = 100 =>

E(100) = 100·(1+2+3+....+200) = 100·(1+200)·200:2 = 100·100·201 = 2010000

E(101) = 101·(1+2+3+......+200) = 101·(1+200)·200:2 = 101·201·100 = 2030100

E(x) ∈ [2.010.000 , 2.030.100]

Answer 2

100≤x≤101 ;  E(x)=|1-x|+|2-x|+...+|200-x|

E(100)=|1-100|+|2-100|+...+|200-100|

E(100)=(99+98+97+.....3+2+1)+0+(1+2+3.....+99)+100  (1)

E(100)=2· (1+2+3.....+99) +100

E(100)=2·99·100/2+100=9900+100

E(100)=10 000

E(101)=|1-101|+|2-101|+...+|200-101|

E(101)=100+(99+98+97+.....3+2+1)+0+(1+2+3.....+99)  (2)

din (1) si (2)=> E(100)=E(101)=10 000