Number with binary number and sum.

Hello teacher~

x_n is a decimal system.

x_1 = 111_(2)
x_2 = 1011_(2)
x_3 = 1101_(2)
x_4 = 1110_(2)
x_5 = 10011_(2)
....
x_120 = 1,110,000,000_(2)

Right side is a binary number with three 1.
and x_1 < x_2 < x_3 < ... < x_120.
Since 10C3 = 120,
it's true that x_120 = 1,110,000,000_(2).

Find x_1 + x_2 + ... + x_120.

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The number of "1" is 3*120 = 360. (from x_1 to x_120)

http://board-2.blueweb.co.kr/user/math565/data/math/bina.jpg
and the number of "1" is 36 in each column with jpg.
Why ??? (For each column, the number of "1" is same ?...so, 360/10)

Anyway,
It means that 36*[1 + 2 + 2^2 + ... + 2^9] is the answer.


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