Question

tính:

\(\dfrac{1.98+2.97+3.96+....+96.3+97.2+98.1}{1.2+2.3+3.4+4.5+.....+98.99}\)

Answer 1

Bải giải

B=$\frac{1.98+2.97+3.96+...+98.1}{1.2+2.3+3.4+...+}$

B=$\frac{1.\left(100-2\right)+2.\left(100-3\right)+3.\left(100-4\right)+...+98.\left(100-99\right)}{1.2+2.3+3.4+...+98.99}$

B=$\frac{100.\left(1+2+3+...+98\right)-\left(1.2+2.3+3.4+...+98.99\right)}{1.2+2.3+3.4+...+98.99}$

B=$\frac{100.\left(1+98\right).98:2}{1.2+2.3+3.4+...+98.99}-\frac{1.2+2.3+3.4+...+98.99}{1.2+2.3+3.4+...+98.99}$

B=$\frac{\mathrm{50.98.99}}{1.2+2.3+3.4+...+98.99}$

Đặt M = 1.2+2.3+3.4+....+98.99

=> 3M=3.(1.2+2.3+3.4+...+98.99)

=> 3M = 1.2.3+2.3.(4-1)+...+098.99.(100-97)

3M= 1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...+98.99.100-97.98.100

3M=98.99.100

=> M = 98.33.100

=> B = $\frac{\mathrm{50.98.99}}{\mathrm{98.33.100}}-1=\frac{3}{2}-1=\frac{1}{2}$