Bài 1: Tìm x
1/1.6 + 1/6.11 + 1/11.16 + .......+ 1/(5x+1) . (5x+6) = 16/81
Bài 2: CMR
a/ 1/1.2.3 + 1/2.3.4 + ........ + 1/18.19.20 < 1/4
b/ 1/22 + 1/32 + 1/42 + .... + 1/n2 < 1
c/ Cho a/b > 0 CMR a/b + b/a lớn hơn hoặc = a
Những câu hỏi liên quan
Tính giá trị biểu thức:
a) A = -11/23.10/-13 +-11/13.3/-23-2/23
b) B = 1/1.2.3 + 1/2.3.4 + ... + 1/18.19.20
c) C = 52/1.6 + 52/6.11 + 52/11.16 +...+ 52/31.35
d) D = 1. 2 .3 + 2 .4. 6+ 4 .8 .12 + 7 .14 .21/ 1. 3. 5 + 2. 6. 10 + 4 .12 .20 + 7 .21 .35 + 3/5
GIÚP MIK VS AK!
\(B=\frac{1}{1\cdot2\cdot3}+\frac{1}{2\cdot3\cdot4}+\frac{1}{3\cdot4\cdot5}+\frac{1}{18\cdot19\cdot20}\)
\(B=\frac{1}{2}\left(\frac{2}{1\cdot2\cdot3}+\frac{2}{2\cdot3\cdot4}+\frac{2}{3\cdot4\cdot5}+\frac{2}{18\cdot19\cdot20}\right)\)
\(B=\frac{1}{2}\left(\frac{1}{1\cdot2}-\frac{1}{2\cdot3}+\frac{1}{2\cdot3}-\frac{1}{3\cdot4}+\frac{1}{3\cdot4}-\frac{1}{4\cdot5}+...+\frac{1}{18\cdot19}-\frac{1}{19\cdot20}\right)\)
\(B=\frac{1}{2}\left(\frac{1}{1\cdot2}-\frac{1}{19\cdot20}\right)\)
\(B=\frac{1}{2}\cdot\frac{189}{380}=\frac{189}{760}\)
\(C=\frac{52}{1\cdot6}+\frac{52}{6\cdot11}+\frac{52}{11\cdot16}+...+\frac{52}{31\cdot36}\)
\(C=\frac{52}{5}\left(\frac{5}{1\cdot6}+\frac{5}{6\cdot11}+\frac{5}{11\cdot16}+...+\frac{6}{31\cdot36}\right)\)
\(C=\frac{52}{5}\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+...+\frac{1}{31}-\frac{1}{36}\right)\)
\(C=\frac{52}{5}\cdot\left(1-\frac{1}{36}\right)\)
\(C=\frac{91}{9}\)
Tính giá trị biểu thức:
a) A = -11/23.10/-13 +-11/13.3/-23-2/23
b) B = 1/1.2.3 + 1/2.3.4 + ... + 1/18.19.20
c) C = 52/1.6 + 52/6.11 + 52/11.16 +...+ 52/31.35
d) D = 1. 2 .3 + 2 .4. 6+ 4 .8 .12 + 7 .14 .21/ 1. 3. 5 + 2. 6. 10 + 4 .12 .20 + 7 .21 .35 + 3/5
GIÚP MIK VS AK! MIK CẦN GẤP LẮM! TKS!
Tính tổng:
A = 1/ 1.2 + 1/ 2.3 + ... + 1/ 999.1000
B = 1/ 1.6 + 1/ 6.11 + .... + 1/ 496.501
C = 1/ 1.2.3 + 1/ 2.3.4 + ..... + 1/ 998.999.1000
A=999/1000
B= ...........
C=..................
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Tìm x :
\(\frac{1}{1.6}+\frac{1}{6.11}+\frac{1}{11.16}+..+\frac{1}{\left(5x+1\right)\left(5x+6\right)}=\frac{10}{41}\)
Ta có :
\(\frac{5}{1.6}+\frac{5}{6.11}+................+\frac{5}{\left(5.x+1\right).\left(5.x+6\right)}=\)\(\frac{50}{41}\)
=> \(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+...............+\frac{1}{5.x+1}-\frac{1}{5.x+6}\) = \(\frac{50}{41}\)
=> \(1-\frac{1}{5.x+6}=\frac{50}{41}\)
=> \(\frac{1}{5.x+6}=\frac{-9}{41}\)................ mình ko tìm ra vì p/s kia ko có tử là 1
bạn xem lại đề bài giúp mình nha
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Tìm x:
Bài 3:
a) 1/3 + 2/3 : x -7
b) 3 1/2 - 1/2 x 2/3
c) [(x + 1/3) * 3/4 +5] : 23
d) (1 2/3 - x). 0,75 - 2 1/2
e) x + 75% x -1,6
f) (x - 2/3) (2x+1) 0
g) 1 - (2x + 1/2) 2 3/4
h) 5/1.6 + 5/6.11 + ... + 5/(5x + 1).(5x + 6) 2020/2021
Giúp mình bài 3 với, ai làm được đúng hết mình sẽ tik hết nhé! Hurry up!
Đọc tiếp
Tìm x:
Bài 3:
a) 1/3 + 2/3 : x = -7
b) 3 1/2 - 1/2 x = 2/3
c) [(x + 1/3) * 3/4 +5] : 2=3
d) (1 2/3 - x). 0,75 - 2 = 1/2
e) x + 75% x = -1,6
f) (x - 2/3) (2x+1) = 0
g) 1 - (2x + 1/2) 2 = 3/4
h) 5/1.6 + 5/6.11 + ... + 5/(5x + 1).(5x + 6) = 2020/2021
Giúp mình bài 3 với, ai làm được đúng hết mình sẽ tik hết nhé! Hurry up!
CMR : A = 1/1.2.3 + 1/2.3.4 + ... + 1/18.19.20 < 1/4
A = 1/1.2.3 + 1/2.3.4 + ... + 1/18.19.20
\(A=\frac{1}{2}.\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{18.19}-\frac{1}{19.20}\right)\)
\(A=\frac{1}{2}.\left(\frac{1}{1.2}-\frac{1}{19.20}\right)\)
\(A=\frac{1}{4}-\frac{1}{2.19.20}< \frac{1}{4}\)
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1) tính :
a) 2/ 1.2.3 + 2/ 2.3.4 + ...+ 2/ 98.99.100
b) 4/ 2.4.6 + 4/ 4.6.8 + ...+ 4/ 50.52.54
c) 8/ 1.3.5 + 8/ 3.5.7 + ...+ 8/ 18.19.20
d) 1/ 1.2.3 + 1/ 2.3.4 + ... + 1/ 18.19.20
so sánh : A= 1/1.6+1/6.11+1/11.16+....+ 1/ (5n+1). (5n+6) với B= n+1/5n+6
Ta có : \(A=\frac{1}{1\cdot6}+\frac{1}{6\cdot11}+\frac{1}{11\cdot16}+...+\frac{1}{(5n+1)(5n+6)}\)
\(=\frac{1}{5}\cdot\left[\frac{5}{1\cdot6}+\frac{5}{6\cdot11}+\frac{5}{11\cdot16}+...+\frac{5}{(5n+1)(5n+6)}\right]\)
\(=\frac{1}{5}\cdot\left[1-\frac{1}{5n+6}\right]=\frac{1}{5}\cdot\frac{5n+6-1}{5n+6}=\frac{1}{5}\cdot\frac{5(n+1)}{5n+6}=\frac{n+1}{5n+6}\)
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Tìm số tự nhiên x thỏa mãn:
a) 5/1.6 + 5/6.11 +...+ 5/(5x + 1).(5x + 6) = 2010/2011
b) 1/3.5 + 1/5.7 + 1/7.9 +...+ 1/(2x + 1).(2x + 3) = 15/93