Răspuns:
Explicație pas cu pas:
a = 1 + 1/2 + 1/2^2 + 1/2^3 + 1/2^4 + 1/2^5
a*1/2 = 1/2 + 1/2^2 + 1/2^3 + 1/2^4 + 1/2^5 + 1/2^6
a - a*1/2 = 1 + 1/2 + 1/2^2 + 1/2^3 + 1/2^4 + 1/2^5 - 1/2 - 1/2^2 - 1/2^3 - 1/2^4 - 1/2^5 - 1/2^6 = 1 - 1/2^6
a - a*1/2 = a*1/2 = 1 - 1/2^6
a = 2*(1 - 1/2^6) = 2 - 2/2^6 = 1 - 1/2^5
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b = (√3 - √5 + √2)(√3 + √5 - √2) + 6 - 2√10
= 3 +√15 -√6 -√15 - 5 + √10 + √6 + √10 - 2 + 6 - 2√10
= 3 - 5 - 2 + 6 = 2
a < b
1 - 1/2^5 < 2
-1 < 1/2^5 adevarat
