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Ta có :
A= 1+ 1/2 + 1/3 +1/4 + ...+ 1/63 + 1/64
=1 + ( 1/2 + 1/3 + 1/4 ) + ( 1/5 +1/6 + ..+1/8 ) + ( 1/9 + 1/10 + ..+ 1/16 ) + ( 1/17 + 1/18 + ...+ 1/32 ) + ( 1/33 + 1/34 + ...+1/63 + 1/64 )
=> A > 1 + ( 1/2 + 1/4.2 ) + 1/8.4 + 1/16.8 + 1/32.16 + 1/64.32
A > 1 + 1/2 + 1/2 + 1/2 +1/2
=>A > 4
Câu b thôi các bạn nhé, câu a mình ko cần nx với cả mình ghi sai dữ liệu câu a r
a, \(\frac{1}{4}\cdot\frac{2}{6}\cdot\frac{3}{8}\cdot\frac{4}{10}\cdot...\cdot\frac{30}{62}\cdot\frac{31}{64}=2x\)
\(\Leftrightarrow\frac{1\cdot2\cdot3\cdot4\cdot...\cdot30\cdot31}{4\cdot6\cdot8\cdot10\cdot...\cdot62\cdot64}=2x\)
\(\Leftrightarrow\frac{1\cdot2\cdot3\cdot4\cdot...\cdot30\cdot31}{2\cdot2\cdot3\cdot2\cdot4\cdot2\cdot5\cdot2\cdot....\cdot31\cdot2\cdot32\cdot2}=2x\)
\(\Leftrightarrow\frac{1}{2\cdot2\cdot2\cdot2\cdot....\cdot2\cdot2\cdot32}=2x\)
Có : (31 - 1) : 1 + 1 = 31 (thừa số 2)
\(\Rightarrow\frac{1}{2^{31}.32}=2x\)
\(\Rightarrow x=\frac{1}{2^{31}.32}\div2\)
b, \(\left(x-1\right)^{x+2}=\left(x-1\right)^{x+4}\)
\(\Leftrightarrow x+1=x+4\)
\(\Leftrightarrow0=3\text{ (vô lý) }\)
\(1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{199}-\frac{1}{200}\)
\(=1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+....+\frac{1}{199}+\frac{1}{200}-2\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+....+\frac{1}{200}\right)\)
\(=1+\frac{1}{2}+\frac{1}{3}+....+\frac{1}{199}+\frac{1}{200}-1-\frac{1}{2}-\frac{1}{4}-....-\frac{1}{100}\)
\(=\left(1+\frac{1}{2}+...+\frac{1}{100}\right)+\left(\frac{1}{101}+...+\frac{1}{199}+\frac{1}{200}\right)-\left(1+\frac{1}{2}+...+\frac{1}{100}\right)\)
\(=\frac{1}{101}+\frac{1}{102}+.....+\frac{1}{199}+\frac{1}{200}\) (ĐPCM)
Ta có : 1 - 1/2 + 1/3 - 1/4 + ....- 1/200
= (1 + 1/3 + 1/5 + ....+ 1/199) - ( 1/2 + 1/4 + 1/6 + .... + 1/200)
= ( 1 + 1/3 +...+ 1/199) + (1/2 +1/4 + ...+ 1/200) - 2(1/2+1/4+...+ 1/200)
= (1+1/2+1/3+....+1/199 + 1/200) - (1 +1/2 +1/3 +....+1/100)
= 1/101 + 1/102+ 1/103 + .... + 1/200
chúc bạn học tốt!!!!!!!
\(\Rightarrow\frac{1}{2.2}.\frac{2}{2.3}.\frac{3}{2.4}.\frac{4}{2.5}.\frac{5}{2.6}...\frac{30}{2.31}.\frac{31}{2.32}=2^x\)
\(\Rightarrow\frac{1}{2^{31}}.\frac{1.2.3.4....31}{2.3.4...32}=2^x\)
\(\Rightarrow\frac{1}{2^{31}}.\frac{1}{32}=2^x\)
\(\Rightarrow\frac{1}{2^{31}.2^5}=2^x\)
\(\Rightarrow\frac{1}{2^{36}}=2^x\Rightarrow x=-36\)
\(=1+\frac{1}{2}+\left(\frac{1}{3}+\frac{1}{4}\right)+\left(\frac{1}{5}+...+\frac{1}{8}\right)+\left(\frac{1}{9}+...+\frac{1}{16}\right)+\left(\frac{1}{17}+...+\frac{1}{32}\right)+\left(\frac{1}{33}+...+\frac{1}{64}\right)\)
\(=1+\frac{1}{2}+\frac{1}{4}.2+\frac{1}{8}.4+\frac{1}{16}.8+\frac{1}{32}.16+\frac{1}{64}.32\)
\(=1+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}\)
\(=1+\frac{1}{2}.6\)
\(=1+3\)
\(=4\)
~~ Bố thí cái li.ke ~~