Tinh nhanh
1+5/4+5/8+5/32+5/64
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\(1+\frac{5}{4}+\frac{5}{8}+\frac{5}{16}+\frac{5}{32}+\frac{5}{64}\)
\(=\frac{64}{64}+\frac{80}{64}+\frac{40}{64}+\frac{20}{64}+\frac{10}{64}+\frac{5}{64}\)
\(=\frac{64+80+40+20+10+5}{64}\)
\(=\frac{219}{64}\)
\(=\frac{27}{8}\)
1+5/4+5/8+5/16+5/32+5/64
=1+5/4+5/8+5/16+5/32+5/64
=1+(5/4+5/8+5/16+5/32+5/64)
=1+[5x(1/4+1/8+1/16+1/32+1/64)]
A=1/4+1/8+1/16+1/32+1/64
2A=1/2+1/4+1/8+1/16+1/32
2A-A=(1/2+1/4+1/8+1/16+1/32)+(1/4+1/8+1/16+1/32+1/64)
A=1/2-1/64
A=31/64
1+[5x31/64]
=1+155/64
=219/64
1: \(5\cdot25\cdot2\cdot16\cdot4=10\cdot25\cdot4\cdot16=10\cdot100\cdot16=16000\)
2: \(25\cdot5\cdot4\cdot2\cdot27\)
\(=25\cdot4\cdot5\cdot2\cdot27\)
\(=100\cdot10\cdot27=27000\)
3: \(2^3\cdot17-2^3\cdot17=2^3\left(17-17\right)=0\)
4: \(58\cdot75+58\cdot50-58\cdot25\)
\(=58\left(75+50-25\right)\)
\(=58\cdot100=5800\)
7: \(5\cdot23+35\cdot41+64\cdot65\)
\(=5\left(23+7\cdot41\right)+64\cdot65\)
\(=5\cdot310+64\cdot65=1550+4160=5710\)
Đặt \(A=1+\frac{5}{4}+\frac{5}{8}+\frac{5}{16}+\frac{5}{32}+\frac{5}{64}\)
\(=5\cdot\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}\right)\)
Đặt \(B=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}\)
\(\Rightarrow2\cdot B=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}\)
\(\Rightarrow B=2\cdot B-B=1-\frac{1}{64}=\frac{63}{64}\)
\(\Rightarrow A=5\cdot\frac{63}{64}=\frac{315}{64}\)
\(E=\frac{5}{4}+\frac{5}{8}+\frac{5}{16}+\frac{5}{32}+\frac{5}{64}\)
\(\Leftrightarrow E=\frac{5}{2^2}+\frac{5}{2^3}+\frac{5}{2^4}+\frac{5}{2^5}+\frac{5}{2^6}\)
\(\Leftrightarrow E=5\left(\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+\frac{1}{2^5}+\frac{1}{2^6}\right)\)
Đặt \(A=\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+\frac{1}{2^5}+\frac{1}{2^6}\)
\(\Rightarrow2A=\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+\frac{1}{2^5}\)
\(\Rightarrow2A-A=\left(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+\frac{1}{2^5}\right)-\left(\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+\frac{1}{2^5}+\frac{1}{2^6}\right)\)
\(\Rightarrow A=\frac{1}{2}-\frac{1}{2^6}\)
Thay \(A=\frac{1}{2}-\frac{1}{2^7}\)vào E ta được:
\(E=5\cdot\left(\frac{1}{2}-\frac{1}{2^6}\right)\)
Bài làm
~ Đề là tính E, mà làm theo cách của bạn Vũ Hà My đây thì nó lại vừa dài, vừa khó ra kết quả. Nên mik sẽ làm theo cách quy đồng nhé. Dấu " . " là dấu nhân nha. ~
\(E=\frac{5}{4}+\frac{5}{8}+\frac{5}{16}+\frac{5}{32}+\frac{5}{64}\)
\(E=5.\left(\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}\right)\)
\(E=5.\left(\frac{16}{64}+\frac{8}{64}+\frac{4}{64}+\frac{2}{32}+\frac{1}{64}\right)\)
\(E=5.\frac{31}{64}\)
\(E=\frac{155}{64}\)
Vậy \(E=\frac{155}{64}\)
1+\(\frac{5}{4}+\frac{5}{8}+\frac{5}{32}+\frac{5}{64}\)
= 3\(\frac{7}{64}\)
= \(\frac{199}{64}\)
\(1+\frac{5}{4}+\frac{5}{8}+\frac{5}{32}+\frac{5}{64}\)
\(=3+\frac{7}{64}\)
\(=\frac{199}{64}\)
Ủng hộ nhé ! Bấm Đúng cho mình nhé ! ^^