Cho A = 1+3+32+.......+399
a. Tính tông A
b. Cmr A : 4 , A : 47
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a) = 25 x 32 + 25 x 47 - 32 x 25 + 32 x 47
= 25 x 47 - 32 x 47
= -329
b) = 2 - 12 - 6
= -16
c) = 2 x (-7) - 10 + 1
= -14 - 10 + 1
= -23
d) = -6 - (-1) + (-2)
= -7
a) 47 + 18 – 26 = 39
b) 3 × 8 : 4 = 24 : 4 = 6
c) 5 × 8 – 32 = 40 – 32 = 8
d) 36 : 4 + 17 = 9 + 17 = 26
a) Ta thấy:
5=2+3
11=5+3x2
20=11+3x3
32=20+3x4
47=32+3x5
65=47+3x6
Ta có tổng sau:
A=2+5+11+.....+47+65
A=2 + (11 + 32 + 47) + 20 + (5 + 65)
A= 2 + 90 + 20 + 70
A=182
(Hình như đề sai ở chỗ: 95->65)
Vậy:
A=2+5+11+.....+47+65=182
ta co \(\frac{a}{1+b^2c}=\frac{a\left(1+b^2c\right)-ab^2c}{1+b^2c}=a-\frac{ab^2c}{1+b^2c}\ge a-\frac{ab\sqrt{c}}{2}\)
=>\(\frac{a}{1+b^2c}\ge a-\frac{b\sqrt{a.ac}}{2}\ge a-\frac{b\left(a+ac\right)}{4}\)
cmtt=>dpcm
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