A=1+1+1+...+1-99
Những câu hỏi liên quan
cmr neu 1/a+1/b+1/c =1/a+b+c thi 1/a^99+1/b^99+1/c^99=1/a^99+b^99+c^99
tinh tong gia tri bieu thuc :
a)A=1+1/3+1/5+...+1/97+1/99/1/1*99+1/3*97+1/5*95+...+1/97*3+1/99*1
b)B=1/2+1/3+1/4+...+1/100/99/1+98/2+97/3+...+1/99
A=99^2015+1/99^2014+1
B=99^2014+1/99^2013+1
so sanh a va b
A = 99^2015 + 1/99^2014 + 1 < 99^2015 + 1 + 98 / 99^2014 + 1 + 98
= 99^2015 + 99 / 99^2014 + 99
= 99(99^2014 + 1) / 99(99^2013+1)
= 99^2014 + 1 / 99^2013 + 1 = B
=> A < B
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tính A= (1+1/3+1/5+...+1/95+1/97+1/99) /(1/1*99+1/3*97+1/5*95+...+1/95*5+1/97*3+1/99*1)
a, Cho A= 1/99 + 2/98 + 3/47 + .......... + 98/2 + 99/1
B= 1/2 + 1/3 + 1/4 + ..........+ 1/99 + 1/100
Tính B/A
b, Cho A= 1/49 + 2/48 + 3/47 +.......+ 48/2 +49/1
B= 1 + 2/3 + 2/4 +......+ 2/49 + 2/50
Tính A/B
a: \(A=\left(\dfrac{1}{99}+1\right)+\left(\dfrac{2}{98}+1\right)+...+\left(\dfrac{98}{2}+1\right)+1\)
\(=\dfrac{100}{99}+\dfrac{100}{98}+...+\dfrac{100}{2}+\dfrac{100}{100}\)
\(=100\cdot\left(\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{100}\right)\)=100B
=>B/A=1/100
b: \(A=\left(\dfrac{1}{49}+1\right)+\left(\dfrac{2}{48}+1\right)+\left(\dfrac{3}{47}+1\right)+...+\left(\dfrac{48}{2}+1\right)+\left(1\right)\)
\(=\dfrac{50}{49}+\dfrac{50}{48}+....+\dfrac{50}{2}+\dfrac{50}{50}\)
\(=50\left(\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{50}\right)\)
\(B=\dfrac{2}{2}+\dfrac{2}{3}+\dfrac{2}{4}+...+\dfrac{2}{49}+\dfrac{2}{50}\)
\(=2\left(\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+...+\dfrac{1}{49}+\dfrac{1}{50}\right)\)
=>A/B=25
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Tính A=1/99+1/98+1/97+...+99/1
\(\Rightarrow\) Tử = (\(\frac{1}{99}\)+1)+(\(\frac{2}{98}\)+1)+ \(\left(\frac{3}{97}+1\right)\)+.....+ \(\left(\frac{97}{3}+1\right)\)+ \(\left(\frac{98}{2}+1\right)\) + 1
= \(\frac{100}{99}\) + \(\frac{100}{98}\) + \(\frac{100}{97}\) + ......\(+\frac{100}{3}\).+ \(\frac{100}{2}\) + \(\frac{100}{100}\)
= 100\(\left(\frac{1}{99}+\frac{1}{98}+\frac{1}{97}+....+\frac{1}{3}+\frac{1}{2}+\frac{1}{100}\right)\)
= 100\(\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{98}+\frac{1}{99}+\frac{1}{100}\right)\) giá trị trong dấu ngoặc bằng mẫu số .
\(\Rightarrow\)Nên kết quả là 100
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Tính nhanh
a.(1+1/2)×(1+1/3)×(1+1/4)×...×(1+1/98)×(1+1/99).
b.1/2×2/3×3/4×...×97/98×98/99×99/100
a,=3/2*4/3*....100/99
=3*4*5*....*100/2*3*...*99
=100/2=50
b, nhân lên băng:
1*2*3*...*99/2*3*...*100=1/100
A=1/100*99-1/99*98-....-1/3*2-1/2*1
\(\Rightarrow A=\frac{1}{99.100}-\left(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{98.99}\right)\)
\(\Leftrightarrow A=\frac{1}{99.100}-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{98}-\frac{1}{99}\right)\)
\(\Rightarrow A=\frac{1}{99.100}-1+\frac{1}{99}\)
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A=1/99+1/98+...+99/1 trên1/2+1/3+...+1/100
\(A=\frac{\frac{1}{99}+\frac{1}{98}+...+\frac{99}{1}}{\frac{1}{2}+\frac{1}{3}+...+\frac{1}{100}}\)
\(A=\frac{\left(\frac{1}{99}+1\right)+\left(\frac{1}{98}+1\right)+...+\left(\frac{98}{2}+1\right)+1}{\frac{1}{2}+\frac{1}{3}+...+\frac{1}{100}}\)
\(A=\frac{\frac{100}{99}+\frac{100}{98}+...+\frac{100}{2}+\frac{100}{100}}{\frac{1}{2}+\frac{1}{3}+...+\frac{1}{100}}\)
\(A=\frac{100\left(\frac{1}{99}+\frac{1}{98}+...+\frac{1}{2}+\frac{1}{100}\right)}{\frac{1}{2}+\frac{1}{3}+...+\frac{1}{100}}\)
\(A=100\)
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Ta có :A =99100+1/9999+1
B=9969+1/9968+1
So sánh A và B