\(\text{Đặt C = 1.2 + 2.3 + 3.4 + ..... +98.99 }\)

\(\text{ Và A = 1.98 + 2.97 + 3.96 + .... + 98.1 }\)

\(\text{Khi đó : }A=1+\left(1+2\right)+....+\left(1+2+...+98\right)\)

                      \(=\frac{1.2}{2}+\frac{2.3}{2}+\frac{3.4}{2}+....+\frac{98.99}{2}\)

                      \(=\frac{1.2+2.3+3.4+....+98.99}{2}=\frac{C}{2}\)

\(\Rightarrow B=\frac{B}{\frac{2}{B}}=\frac{1}{2}\)

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

thanks

tử số của E=1 +(1+2)+(1+2+3)+.....+(1+2+3+..+98)

=1.2/2  +2.3/2 +3.4/2 +.....+98.99/2

=1.2+2.3+3.4+...+98.99/2

=>E=1/2 (đpcm)

tử số của E=1 +(1+2)+(1+2+3)+.....+(1+2+3+..+98)

=1.2/2  +2.3/2 +3.4/2 +.....+98.99/2

=1.2+2.3+3.4+...+98.99/2

=>E=1/2 (đpcm)

tử số của E=1 +(1+2)+(1+2+3)+.....+(1+2+3+..+98)

=1.2/2  +2.3/2 +3.4/2 +.....+98.99/2

=1.2+2.3+3.4+...+98.99/2

=>E=1/2 (đpcm)

\(2\)

or\(\frac{1}{2}\)