tính B

\(\frac{T}{M}=\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{100}}{\frac{1}{99}+\frac{2}{98}+...+\frac{98}{2}+\frac{99}{1}}\)

Xét M - 99 + 98 = \(\frac{100}{99}+\frac{100}{98}+...+\frac{100}{2}\)

\(\Leftrightarrow M-1=100\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{99}\right)\)

\(\Rightarrow M=\frac{100}{100}+100\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{99}\right)=100\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{100}\right)\)

\(\Rightarrow\frac{T}{M}=\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{100}}{100\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{100}\right)}=\frac{1}{100}\)

Đặt A 

=> 4 x A = 1 x 2x 3 x 4+2 .3 .4.4 + .........+ 97. 98 . 99 . 4 + 98 . 99 . 100

=> 4 x A = 1 . 2 .3 . (4 - 0) + 2 . 3 . 4 . (5 - 1) + ........+ 97 . 98 . 99 . (100 - 96 ) + 98 .99 .100 . (101 - 97 )

=> 4 x A = 1 . 2 .3 . 4 - 0. 1 .2 .3 + 2. 3. 4 .5 - 1.2 .3 .4 + ..........+ 97 . 98 . 99. 100 - 96 . 97 .98. 99 + 98 .99 . 100 .101 -97 .98 .99. 100

=> 4 x A = 98 . 99 .100 - 0. 1 .2 .3 

=>  A      = \(\frac{98.99.100-6}{4}\)

=> A       = 242548.5

Tick cho tớ nha 

Sửa lại đoạn cuối câu trả lời trên:

4A=98*99*100*101

=> A=\(\frac{98\cdot99\cdot100\cdot101}{4}=24497550\)(do 0*1*2*3=0)

thằng thứ 2 đúng

Thao khảm:

 

=1.100/99.98/99.....2/1

=1.100

=100

Sửa đề: \(-1+3-5+7-...-97+99\)

1) Ta có: \(-1+3-5+7-...-97+99\)

\(=\left(-1+3\right)+\left(-5+7\right)+...+\left(-97+99\right)\)

\(=2+2+...+2=2\cdot50=100\)

2) Ta có: \(1+2-3-4+...+97+98-99-100\)

\(=\left(1+2-3-4\right)+\left(5+6-7-8\right)+...+\left(97+98-99-100\right)\)

\(=\left(-4\right)+\left(-4\right)+...+\left(-4\right)\)

\(=\left(-4\right)\cdot25=-100\)