Question

Đã trả lời bởi chuyên gia

Answer 1

a)

Đặt

$X = \frac{10}{3} + \frac{10}{6} + \frac{10}{12} + \frac{10}{24} + \frac{10}{48} + \frac{10}{96} = \frac{10}{3} . (1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{16} + \frac{1}{32}) = \frac{10}{3} . (1 + \frac{1}{2} + \frac{1}{2^{2}} + \frac{1}{2^{3}} + \frac{1}{2^{4}} + \frac{1}{2^{5}}) Đặt : A = 1 + \frac{1}{2} + \frac{1}{2^{2}} + \frac{1}{2^{3}} + \frac{1}{2^{4}} + \frac{1}{2^{5}} \Rightarrow 2 A = 2 + 1 + \frac{1}{2} + \frac{1}{2^{2}} + \frac{1}{2^{3}} + \frac{1}{2^{4}} \Rightarrow 2 A - A = 3 + \frac{1}{2} + \frac{1}{2^{2}} + \frac{1}{2^{3}} + \frac{1}{2^{4}} - (1 + \frac{1}{2} + \frac{1}{2^{2}} + \frac{1}{2^{3}} + \frac{1}{2^{4}} + \frac{1}{2^{5}}) \Leftrightarrow A = 3 - \frac{1}{2^{5}} = 3 - \frac{1}{96} = \frac{287}{96} \Rightarrow X = \frac{10}{3} . \frac{287}{96} = \frac{1435}{144}$

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Answer 2

a)

Đặt

$X = \frac{10}{3} + \frac{10}{6} + \frac{10}{12} + \frac{10}{24} + \frac{10}{48} + \frac{10}{96} = \frac{10}{3} . (1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{16} + \frac{1}{32}) = \frac{10}{3} . (1 + \frac{1}{2} + \frac{1}{2^{2}} + \frac{1}{2^{3}} + \frac{1}{2^{4}} + \frac{1}{2^{5}}) Đặt : A = 1 + \frac{1}{2} + \frac{1}{2^{2}} + \frac{1}{2^{3}} + \frac{1}{2^{4}} + \frac{1}{2^{5}} \Rightarrow 2 A = 2 + 1 + \frac{1}{2} + \frac{1}{2^{2}} + \frac{1}{2^{3}} + \frac{1}{2^{4}} \Rightarrow 2 A - A = 3 + \frac{1}{2} + \frac{1}{2^{2}} + \frac{1}{2^{3}} + \frac{1}{2^{4}} - (1 + \frac{1}{2} + \frac{1}{2^{2}} + \frac{1}{2^{3}} + \frac{1}{2^{4}} + \frac{1}{2^{5}}) \Leftrightarrow A = 3 - \frac{1}{2^{5}} = 3 - \frac{1}{96} = \frac{287}{96} \Rightarrow X = \frac{10}{3} . \frac{287}{96} = \frac{1435}{144}$

Answer 3

a)

Đặt

X=103+106+1012+1024+1048+1096=103.(1+12+14+18+116+132)=103.(1+12+122+123+124+125) Đặt : A=1+12+122+123+124+125⇒2A=2+1+12+122+123+124⇒2A−A=3+12+122+123+124−(1+12+122+123+124+125)⇔A=3−125=3−196=28796⇒X=103.28796=1435144X=103+106+1012+1024+1048+1096=103.1+12+14+18+116+132=103.1+12+122+123+124+125 Đặt : A=1+12+122+123+124+125⇒2A=2+1+12+122+123+124⇒2A-A=3+12+122+123+124-1+12+122+123+124+125⇔A=3-125=3-196=28796⇒X=103.28796=1435144

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