Câu 2:

A = 1.3 + 3.5 + 5.7 + ...+ 97.99 + 99.100

A = (1.3 + 3.5 + 5.7 + ...+ 97.99) + 99.100

Đặt B = 1.3 + 3.5 + 5.7 + ...+ 97.99

6B = B = 1.3 + 3.5 + 5.7 + ...+ 97.99

6B = 1.3.6 + 3.5.6 + ...+ 97.99.6

6B = 1.3.(5+1) . 3.5.(7-1) + ..+97.99.(101-95)

6B = 1.3.5 + 1.3.1 +3.5.7- 1.3.5 +...+97.99.101-95.99.97

6B = 1.3.1 + 97.99.101

6B = 3 + 969903

6B = 969906

B = 969906 : 6

B = 161651

A = 161651 + 99.100

A = 161651 + 9900

A = 171551

Câu 3:

A = A = 2.4 + 4.6 + 6.8 +...+ 98.100 + 100.102

6A = 2.4.6 + 4.6.6 +..+98.100.6 + 100.102.6

6A = 2.4.6 + 4.6.(8-2) +...+100.102.(104 - 98)

6A = 2.4.6 + 4.6.8 - 2.4.6 + ...+ 100.102.104 - 98.100.102

6A = 100.102.104

A = 100.102.104 : 6

A = 10200.104 : 6

A = 1060800 : 6

A = 176800

6^2.(6+3)+3^3/-13=36.3^2+3^3/-13=3^2(36+3)/-13=9.39/-13=-27

2^10.3^8-2.3^9.2^9 / 2^10.3^8+3^8.2^8.2^2.5

=2^10.3^8(1-3) / 2^10.3^8(1+5)

=-2/6=-1/3

a)\(\frac{4^5.9^4-2.6^9}{2^{10}.3^8+6^8.20}=\frac{\left(2^2\right)^5.\left(3^2\right)^4-2.\left(2.3\right)^9}{2^{10}.3^8+\left(3.2\right)^8.2^2.5}=\frac{2^{10}.3^8-2.2^9.3^9}{2^{10}.3^8+3^8.2^8.2^2.5}=\frac{2^{10}.3^8-2^{10}.3^9}{2^{10}.3^8+3^8.2^{10}.5}\)

\(=\frac{2^{10}.3^8.\left(1-3\right)}{2^{10}.3^8.\left(1+5\right)}=\frac{-2}{6}=\frac{-1}{3}\)

b) đặt A=2¹⁰⁰ - 2⁹⁹ + 2⁹⁸ - 2⁹⁷ +...+ 2² - 2

=>2A=2¹⁰¹-2¹⁰⁰+2⁹⁹-2⁹⁸+...+2³-2²

=>2A+A=2¹⁰¹-2¹⁰⁰+2⁹⁹-2⁹⁸+...+2³-2²+2¹⁰⁰ - 2⁹⁹ + 2⁹⁸ - 2⁹⁷ +...+ 2² - 2

=>3A=2¹⁰¹-2

=>A=\(\frac{2^{101}-2}{3}\)

thank kiu 

thank kiu

...............

\(1^2+2^2+3^2+...+99^2+100^2\)

\(=1+2\left(1+1\right)+3\left(2+1\right)+99\left(98+1\right)+100\left(99+1\right)\)

\(=1+1.2+2+2.3+3+...+98.99+99+99.100+100\)

\(=\left(1.2+2.3+3.4+...+99.100\right)+\left(1+2+3+...+99+100\right)\)

\(=333300+5050\)

\(=338050\)

Cảm ơn nhiều !