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7/7 = 1
5/6 < 8/9
2/9 < 1
4/5 > 3/7
4 > 9/5
25/75 < 50/100
t.i.c.k mình nhoa !
122 =14
132 <12.3
.............
11002 <199.100
⇒A<14 +12.3 +....+199.100
⇒A<14 +12 −13 +...+199 −1100
⇒A<14 +12 −1100
⇒A<14 <34
\(A=\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{100^2}\)
\(A>\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+...+\frac{1}{100\cdot101}\)
\(A>\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{100}-\frac{1}{101}\)
\(A>\frac{1}{2}-\frac{1}{101}=\frac{99}{202}>\frac{2}{3}\)
\(\Rightarrow A>\frac{2}{3}\)
\(Giải\)
\(\Rightarrow A=\frac{1}{2}-\frac{1}{2}+\frac{1}{3}-\frac{1}{3}\)\(+\frac{1}{4}-\frac{1}{4}+...+\frac{1}{2014}-\frac{1}{2014}\)
\(A=0+0+0+...+0+0\)
\(\Rightarrow A=0\)
\(a.\)\(A< 1\)
b. \(A< \frac{3}{4}\)
\(\left(1-\frac{1}{4}\right)\left(1-\frac{1}{9}\right)\left(1-\frac{1}{16}\right)\left(1-\frac{1}{25}\right)...\left(1-\frac{1}{10000}\right)\)
\(=\frac{3}{4}\cdot\frac{8}{9}\cdot\frac{15}{16}\cdot\frac{24}{25}\cdot...\cdot\frac{9999}{10000}\)
\(=\frac{\left(1\cdot3\right)\left(2\cdot4\right)\left(3\cdot5\right)\left(4\cdot6\right)...\left(99\cdot101\right)}{\left(2\cdot2\right)\left(3\cdot3\right)\left(4\cdot4\right)\left(5\cdot5\right)...\left(100\cdot100\right)}\)
\(=\frac{\left(1\cdot2\cdot3\cdot4\cdot...\cdot99\right)\left(3\cdot4\cdot5\cdot6\cdot...\cdot101\right)}{\left(2\cdot3\cdot4\cdot5\cdot...\cdot100\right)\left(2\cdot3\cdot4\cdot5\cdot...\cdot100\right)}\)
\(=\frac{1\cdot101}{100\cdot2}\)
\(=\frac{101}{200}\)
a.5/6 - 26/5 X 1/13 = 13/30
b.( 19/23 - 22/46 ) X 23/46 = 3/23
c.25/8 x 14/30 = 35/24
d.( 3/4 x 5/7 ) x ( 20/9 x 14/15 ) = 10/9
e.4/35 x 25/32 x 38/24 = 95/672
g. 1/2 x 3/4 x 2/3 x 4/5 = 1/5
h.5/6 x 11/4 - 5/4 x 23/6 = -5/2
i.9/16 x 13/4 - 9/4 x 5/16 + 9/16 x 17/4 = 225/64
k.( 7 x 1/3 ) x ( 1/7 x 6 ) = 2
m.2/3 x ( 3/5 + 3/7 ) = 34/35
n.4/5 x ( 5/8 + 7/4 ) = 19/10
p.( 1/33 + 31/333 - 341/3333 ) x ( 1/2 - 1/3 - 1/6 ) = 0
mih giành cả nửa tiếng để giải đó , k nha
Mình không chắc đã đúng đâu nhưng mình cứ giair thử nhé !
Ta có :
A = \(\frac{1}{1}-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}\)+ ... + \(\frac{1}{99}-\frac{1}{100}\)
= \(\left(\frac{1}{1}+\frac{1}{3}+\frac{1}{5}+...\frac{1}{99}\right)\)- \(\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{6}...+\frac{1}{100}\right)\)
= \(\left(\frac{1}{1}+\frac{1}{3}+\frac{1}{5}+...\frac{1}{99}\right)\)+ \(\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{6}...+\frac{1}{100}\right)\)
- \(\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+...+\frac{1}{100}\right)\)x 2
= \(\left(\frac{1}{1}+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{100}\right)\)- \(\left(\frac{1}{1}+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{50}\right)\)
= \(\frac{1}{51}+\frac{1}{52}+\frac{1}{53}+...+\frac{1}{100}\)= B
Vậy , A = B
~ Chúc bạn học giỏi ! ~