\(A=\frac{1^2.2^2.3^2...1000^2}{1.2^2.3^2.4^2...1000^2.1001}=\frac{1}{1001}\)

1² /1.2 . 2²/2.3 . 3²/3.4 ...  999²/999.1000

= 1.1/1.2 . 2.2/2.3 . 3.3/3.4........... 999.999/999.1000

= 1/2. 2/3 . 3.4.....999/1000

= 1/1000

thanks

\(A=\frac{1^2}{1.2}.\frac{2^2}{2.3}.\frac{3^2}{3.4}.....\frac{100^2}{1000.1001}\)

\(A=\frac{1.1.2.2.3.3.....1000.1000}{1.2.2.3.3.4.....1000.1001}\)

\(A=\frac{\left(1.2.3.....1000\right).\left(1.2.3.....1000\right)}{\left(1.2.3.4....1000\right).\left(2.3.4.....1001\right)}\)

\(A=\frac{1}{1001}\)

Ta có A=\(\frac{1^2}{1.2}.\frac{2^2}{2.3}.\frac{3^2}{3.4}.....\frac{1000^2}{1000.1001}\)

           =\(\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.....\frac{1000}{1001}\)

           =\(\frac{1.2.3.....1000}{2.3.4.....1001}\)

           =\(\frac{1}{1001}\)

Trä Loi Bhangra nhé

S = 2/1×2 + 2/2×3 + 2/3×4 + 2/4×5 + ... + 2/101×102

B = 2 × (1/1×2 + 1/2×3 + 1/3×4 + 1/4×5 + ... + 1/101×102)

B = 2 × (1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + ... + 1/101 - 1/102)

B = 2 × (1 - 1/102)

B = 2 × 101/102

B = 101/51

\(\frac{2}{1.2}+\frac{2}{2.3}+\frac{2}{3.4}+....+\frac{2}{100.101}\)

\(=2.\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+....+\frac{1}{100.101}\right)\)

\(=2.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+.....+\frac{1}{100}-\frac{1}{101}\right)\)

\(=2.\left(1-\frac{1}{101}\right)\)

\(=2.\frac{100}{101}=\frac{200}{101}\)

\(\frac{2}{1\cdot2}+\frac{2}{2\cdot3}+\frac{2}{3\cdot4}+........+\frac{2}{8\cdot9}+\frac{2}{9\cdot10}\)

\(=2\cdot\left(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+......+\frac{1}{8\cdot9}+\frac{1}{9\cdot10}\right)\)

\(=2\cdot\left(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+........+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}\right)\)

\(=2\cdot\left(\frac{1}{1}-\frac{1}{10}\right)\)

\(=2\cdot\frac{9}{10}=\frac{9}{5}\)

đúng nha !

Ta có:

2/1.2+2/2.3+2/3.4+2/4.5+2/5.6+2/6.7+2/7.8+2/8.9+2/9.10

=2.(1/1.2+1/2.3+1/3.4+1/4.5+1/5.6+1/6.7+1/7.8+1/8.9+1/9.10)

=2.(1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10)

=2.(1-1/10)

=2.9/10

=9/5

=2(1/1.2+1/2.3+1/3.4+...+1/9.10)=2(1/1-1/2+1/2-1/3+...+1/9-1/10)=2(1/1-1/10)=2.9/10=9/5

tích đúng cho mk đấy nhá

co tui ne

2 kết bạn với mình nhé

bai nay = 2 

nhớ kb nha

Ta có: A = 1.2.3+3.4.5+5.6.7+...+99.100.101

A = 1.3 (5-3) + 3.5 (7-3) + 5.7 (9-3) + ............ + 99.101 (103 - 3)

A = (1.3.5 + 3.5.7 + 5.7.9 + .......... + 99.101.103) - (1.3.3 + 3.5.3 + ....... + 99.101.3)

A = (15+99.101.103.105) : 8 - 3.(1.3 + 3.5 +5.7 + ...... + 99.101)

A = 13517400 - 3.171650

A = 13002450

1.2.3.4+2.3.4.5+3.4.5.6+...+97.98.99.100

4S=(1.2.3+2.3.4+3.4.5+4.5.6+...+98.99.100). 4

4S=1.2.3(4-0)+2.3.4(5-1)+3.4.5(6-2)+4.5.6(7-3)+...+98.99.100(101-97)

4S=1.2.3.4+2.3.4.5-1.2.3.4+3.4.5.6-2.3.4.5+4.5.6.7-3.4.5.6+...98.99.100.101-97.98.99.100

4S=1.2.3.4-1.2.3.4+2.3.4.5-2.3.4.5+3.4.5.6-3.4.5.6+...+97.98.99.100-97.98.99.100+98+99.100+101

4S=98.99.100.101

Vậy S = 98.99.100.101/4 = 24497550