Răspuns:
a = -22/39
b = 11/4
Explicație pas cu pas:
a)
a = (-3/4 - 1/8 : 3/4) : (+13/8) = (-3/4 - 1/8 ·4/3) : (13/8) =
= (⁶⁾-3/4 - 4/24) : (13/8) = (-18-4)/24 : (13/8) =
= -22/24 · 8/13 = -11/12 · 8/13 = -11·8 /(12·13) =
= -11·2/(3·13) = -22/39
a = -22/39
======================
b)
b = (1/1·2 + 1/2·3 +.....+1/99·100) :[(3/5)⁴·(3/5)³:(3/5)⁵] =
= ........
b = x : y
1/1·2 = ²⁾1/1 - 1/2 = (2-1)/2 = 1/2
1/2·3 = ³⁾1/2 - ²⁾1/3 = (3-2)/6 = 1/6
1/3·4 = ⁴⁾1/3-³⁾1/4 = (4-3)/12 = 1/12
......
1/99·100 = ¹⁰⁰⁾1/99 - ⁹⁹⁾1/100 = (100-99)/9900 = 1/9900
x = (1/1·2 + 1/2·3 +.....+1/99·100) =
= 1/1 - 1/2 + 1/2 -1/3 +1/3 - 1/4 +.....+1/99 - 1/100 = 1/1 - 1/100 = 99/100
y = [(3/5)⁴·(3/5)³:(3/5)⁵] = (3/5)⁴⁺³⁻⁵ = (3/5)² = 9/25
x : y = 99/100 : 9/25 = 99/100 ·25/9 = 99·25/(9·100) = 11/4
b = 11/4
