cho ti

\(G=9\cdot\left(\frac{4}{1\cdot3\cdot5}+\frac{4}{3\cdot5\cdot7}+\frac{4}{5\cdot7\cdot9}+....+\frac{4}{25\cdot27\cdot29}\right)\)

\(G=9\cdot\left(\frac{1}{1\cdot3}-\frac{1}{3\cdot5}+\frac{1}{3\cdot5}-\frac{1}{5\cdot7}+.....+\frac{1}{25\cdot27}-\frac{1}{27\cdot29}\right)\)

\(G=9\cdot\left(\frac{1}{1\cdot3}-\frac{1}{27\cdot29}\right)\)

\(G=9\cdot\left(\frac{1}{3}-\frac{1}{783}\right)\)

\(G=9\cdot\left(\frac{261}{783}-\frac{1}{783}\right)\)

\(G=9\cdot\frac{260}{783}\)

\(G=\frac{260}{87}\)

1.3.5+3.5.7+5.7.9+...+97.99.101

=(101-2).(101-1).101.(101+1):4

=25497450

\(A=\frac{1}{1.3}-\frac{1}{3.5}+\frac{1}{3.5}-\frac{1}{5.7}+...+\frac{1}{1997.1999}-\frac{1}{1999.2001}\)

     \(=\frac{1}{1.3}-\frac{1}{1999.2001}\)

       Bạn tính kết quả nhé

a) 9 + 99 + 999 + ... + 999999

= (10 - 1) + (100 - 1) + (1000 - 1) + ... + (1000000 - 1)

= (10¹ + 10² + 10³ + ... + 10⁶) - (1.6)

= 1111110 - 6 = 1111104

b) 1 + 11 + 111 + ... + 1111111

= 1 + (10¹ + 1) + (10² + 10¹ + 1) + ... + (10⁶ + 10⁵ + 10⁴ + 10³ + 10² + 10¹ + 1)

= 10¹ . 6 + 10² . 5 + 10³ . 4 + ... + 10⁶. 1) + (1 + 1.6)

= 60 + 500 + 4000 + ... + 1000000 + 7

= 1234560 + 7 = 1234567

c) C = 1.2 + 2.3 + 3.4 + 4.5 + ... + 98.99

3C = 1.2.3 + 2.3.3 + 3.4.3 + 4.5.3 + ... + 98.99.3

3C = 1.2.3 + 2.3.(4 - 1) + 3.4.(5 - 2) + ... + 98.99.(100 - 97)

3C = 1.2.3 + 2.3.4 - 2.3.1 + 3.4.5 - 3.4.2 +...+ 98.99.100 - 98.99.97

3C = 98.99.100

C = \(\dfrac{98.99.100}{3}\) = 323400

d) D = 1.3.5 + 3.5.7 + 5.7.9 + ... + 95.97.99

8D = 1.3.5.8 + 3.5.7.8 + 5.7.9.8 + ... + 95.97.99.8

8D = 1.3.5.(7 + 1) + 3.5.7.(9 - 1) + 5.7.9.(11 - 3) + ... + 95.97.99.(101 - 93)

8D = 1.3.5.7 + 1.3.5.1 + 3.5.7.9 - 3.5.7.1 + 5.7.9.11 - 5.7.9.3 + ... + 95.97.99.101 - 95.97.99.93

8D = 1.3.5.1 + 95.97.99.101

D = \(\dfrac{1.3.5.1+95.97.99.101}{8}=15517600\)