Question

Aflați x din egalitatea (2013^0+1+2+2^2+2^3+...... +2^100)•x=2^101

Answer 1

(2013^0+1+2+2^2+2^3+...... +2^100)•x=2^101

notăm :

S = 1 + 2 + 2^2 + 2^3 +... + 2^100

S =2^0 + 2^1 + 2^2 +2^3 + ...+ 2^99 + 2^100 | ×2

2 × S = 2^1+2^2+2^3+2^4+...+2^100+2^101

2×S - S = 2^101 - 2^0

S = 2^101 - 1


(2013^0 + S) × x = 2^101

( 1 + 2^101 - 1) × x = 2^101

2^101 × x = 2^101

x = 1
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