Question

Find the minimum value of

Answer 1

\[\huge \left| x-1 \right|+\left| x-2 \right|.......\left| x-10 \right|\]

Answer 2

Deja vu !

Answer 3

yes but i don't remember it

Answer 4

i am getting 5.5 as the answer how to check on wolfram alpha

Answer 5

minimum value occurs at x = 5.5,
minimum value = 25

Answer 6

http://www.wolframalpha.com/input/?i=%5Csum%5Climits_%7Bn%3D1%7D%5E10+abs%285.5-n%29

Answer 7

how come you got it

Answer 8

used symmetry : take the mid value between 1 and 10 : (1+10)/2 = 5.5

Answer 9

and the value

Answer 10

find the half sum first

Answer 11

first 5 terms :

4.5 + 3.5 + .... + 0.5
= 5(0.5) + 4+3+.. +1
= 2.5 + 4(5)/2
= 2.5 + 10
= 12.5

Answer 12

take twice :
2(12.5) = 25

the minimum value of given expression

Answer 13

how many smart cents does it require to unlock the title