Question

B=\(\frac{1.98+2.97+3.96+...+98.1}{1.2+2.3+3.4+...+98.99}\)

Answer 1

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=\(\frac{50.98.99}{1.2+2.3+3.4+...+98.99}\)

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 = \(\frac{50.98.99}{98.33.100}-1=\frac{3}{2}-1=\frac{1}{2}\)

Answer 2

thanks

Answer 3

B=1.(100−2)+2.(100−3)+3.(100−4)+...+98.(100−99)1.2+2.3+3.4+...+98.991.2+2.3+3.4+...+98.991.(100−2)+2.(100−3)+3.(100−4)+...+98.(100−99)​

B=100.(1+2+3+...+98)−(1.2+2.3+3.4+...+98.99)1.2+2.3+3.4+...+98.991.2+2.3+3.4+...+98.99100.(1+2+3+...+98)−(1.2+2.3+3.4+...+98.99)​

B=100.(1+98).98:21.2+2.3+3.4+...+98.99−1.2+2.3+3.4+...+98.991.2+2.3+3.4+...+98.991.2+2.3+3.4+...+98.99100.(1+98).98:2​−1.2+2.3+3.4+...+98.991.2+2.3+3.4+...+98.99​

B=50.98.991.2+2.3+3.4+...+98.991.2+2.3+3.4+...+98.9950.98.99​

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 = 50.98.9998.33.100−1=32−1=1298.33.10050.98.99​−1=23​−1=21