The sum of all the digits of the first 20 terms of this string is

Algebra Level 2

Consider the sequence of binary numbers 101, 1010101, 10101010101,101010101010101.. ..

Find the sum of all the digits of the first 20 terms of this string.

420 105 840 210

Lucas Sousa by Lucas Sousa , 26, Brazil

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1 solution

展豪 張
Apr 28, 2016

The sum = 2 + 4 + ⋯ + 40 = 2 ( 1 + 2 + ⋯ + 20 ) = 2 × 20 × 21 2 = 420 =2+4+\cdots+40=2(1+2+\cdots+20)=2\times \dfrac{20\times21}2=420

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