= 2/1x3/16x4/15x5/1

= 2x3x4x5/1x16x15x1

=2x3x4x5/1x2x8x3x5x1

ở đó bạn chỉ cần gạch 1 số ở phần tử số và gạch 1 số ở phần mẫu số nhớ là giống nhau nhé 

= 1/2

A=1-1/2+1/2-1/3+1/3-1/4+...+1/64-1/128

A=1-1/128

A=127/128

Vậy A=\(\frac{127}{128}\)

B=1-1/2+1/2-1/3+1/3-1/4+...+1/99-1/100

B=1-1/100

B=99/100

Vậy B=\(\frac{99}{100}\)

Ta có A = (3² + 1)(3⁴ + 1)(3⁸ + 1)(3¹⁶ + 1)(3³² + 1)(3⁶⁴ + 1)

=> 8A = 8(3² + 1)(3⁴ + 1)(3⁸ + 1)(3¹⁶ + 1)(3³² + 1)(3⁶⁴ + 1)

=> 8A = (3² - 1)(3² + 1)(3⁴ + 1)(3⁸ + 1)(3¹⁶ + 1)(3³² + 1)(3⁶⁴ + 1)

=> 8A = (3⁴ - 1)(3⁴ + 1)(3⁸ + 1)(3¹⁶ + 1)(3³² + 1)(3⁶⁴ + 1)

=> 8A = (3⁸ - 1)(3⁸ + 1)(3¹⁶ + 1)(3³² + 1)(3⁶⁴ + 1)

=> 8A = (3¹⁶ - 1)(3¹⁶ + 1)(3³² + 1)(3⁶⁴ + 1)

=> 8A = (3³² - 1)(3³² + 1)(3⁶⁴ + 1)

=> 8A = (3⁶⁴ - 1)(3⁶⁴ + 1)

=> 8A = 3¹²⁸ - 1 (1)

Đặt B = 3¹²⁶

=> 8B = 3¹²⁶ . 8 = 3¹²⁶.(3² - 1) = 3¹²⁸ - 3¹²⁶ (2)

Từ (1)(2) => 8A > 8B 

=> A > B 

Tính không quy đồng mẫu:

\(A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{8}+...+\frac{1}{32}-\frac{1}{64}\)

\(A=1-\frac{1}{64}=\frac{63}{64}\)

A = 32 + 16 + 8 + 4 + 2 + 1/64 = 63/64

P/s nhỏ

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1) 1/1.2 + 1/2.3 + ... + 1/6.7

= 1 - 1/2 + 1/2 - 1/3 + ... + 1/6 - 1/7

= 1 - 1/7

= 6/7

2) 1/2 + 1/6 + 1/12 + .. + 1/72

= 1/1.2 + 1/2.3 + 1/3.4 + ... + 1/8.9

= 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/8 - 1/9

= 1 - 1/9

= 8/9

3) \(\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right)...\left(1-\frac{1}{2019}\right)\)

= \(\frac{1}{2}.\frac{2}{3}...\frac{2019}{2020}\)

= \(\frac{1.2....2019}{2.3...2020}\)

= \(\frac{1}{2020}\)

4) A = \(\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+...+\frac{1}{512}\)

       = \(\frac{1}{2^2}+\frac{2}{2^3}+\frac{1}{2^4}+...+\frac{1}{2^9}\)

=> 2A = \(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^8}\)

Lấy 2A - A = \(\left(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^8}\right)-\left(\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+...+\frac{1}{2^9}\right)\)

             A  = \(\frac{1}{2}-\frac{1}{2^9}\)

A = 1 - 1/2 + 1/2 - 1/4 + 1/4 - 1/8 + 1/8 - 1/16 + 1/16 - 1/32 + 1/32 - 1/64

A = 1 - 1/64 

A = 63/64

A = 1/2 + 1/4 +1/8+ 1/16 +1/32 +1/64

A = 1- 1/2 + 1/2 - 1/4 + 1/4 - 1/8 + 1/8 - 1/16 + 1/16 - 1/32 + 1/32 - 1/64

A = 1 - 1/64

A = 63/64

A=1/2+1/4+1/8+1/16+1/32+1/64

A=32/64+16/64+8/64+4/64+2/64+1/64

A=32+16+8+4+2+1/64

A=63/64

\(A=\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{9}+\dfrac{1}{16}+\dfrac{1}{32}+\dfrac{1}{64}\)

\(\dfrac{4}{2}A=\dfrac{4}{2}\cdot\left(\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}+\dfrac{1}{16}+\dfrac{1}{32}+\dfrac{1}{64}\right)\)

\(2A=1+\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}+\dfrac{1}{16}+\dfrac{1}{32}\)

\(2A-A=\left(1+\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}+\dfrac{1}{16}+\dfrac{1}{32}\right)-\left(\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}+\dfrac{1}{16}+\dfrac{1}{32}+\dfrac{1}{64}\right)\)

\(A=\left(\dfrac{1}{2}-\dfrac{1}{2}\right)+\left(\dfrac{1}{4}-\dfrac{1}{4}\right)+..\left(\dfrac{1}{32}-\dfrac{1}{32}\right)+\left(1-\dfrac{1}{64}\right)\)

\(A=1-\dfrac{1}{64}\)

\(A=\dfrac{63}{64}\)

\(\dfrac{127}{128}\)

A=21​+41​+91​+161​+321​+641​

42�=42⋅(12+14+18+116+132+164)24​A=24​⋅(21​+41​+81​+161​+321​+641​)

2�=1+12+14+18+116+1322A=1+21​+41​+81​+161​+321​

2�−�=(1+12+14+18+116+132)−(12+14+18+116+132+164)2A−A=(1+21​+41​+81​+161​+321​)−(21​+41​+81​+