Cho A = 1.2 + 2.3 + ...+ 99.100

=> 3A = 1.2 .3 + 2.3.3 + ...+ 99.100.3

3A = 1.2.( 3-0) + 2.3.(4-1) + ....+ 99.100.( 101 - 98)

3A = 1.2.3 + 2.3.4 - 1.2.3 + ...+ 99.100.101 - 98.99.100

3A = ( 1.2.3 + 2.3.4 + 99.100.101) - ( 1.2.3 + ....+ 98.99.100)

3A = 99.100.101

=> A = 99.100.101 . 1/3

thay A vào B

\(B=(\frac{99.100.101.\frac{1}{3}}{99.100.101}):\frac{1}{3}\)

\(B=\frac{1}{3}:\frac{1}{3}\)

\(B=1\)

\(B=\left(\frac{1.2+2.3+...+99.100}{99.100.101}\right)\div\frac{1}{3}\)

\(\text{Đặt}:C=1.2+2.3+...+99.100\)

\(\Rightarrow3C=1.2.3+2.3.3+...+99.100.3\)

\(\Rightarrow3C=1.2.3+2.3.\left(4-1\right)+...+99.100.\left(101-98\right)\)

\(\Rightarrow3C=1.2.3+2.3.4+...+99.100.101\)

\(\Rightarrow3C=\left(1.2.3+2.3.4+...+99.100.101\right)\)\(-\)\(\left(1.2.3+2.3.4+....+98.99.100\right)\)

\(\Rightarrow3C=99.100.101\)

\(\Rightarrow C=\frac{99.100.101}{3}\)

Thay C vào biểu thức B ta được : 

\(B=\left(\frac{\frac{99.100.101}{3}}{99.100.101}\right)\div\frac{1}{3}=\frac{1}{3}\div\frac{1}{3}=1\)

Vậy B= \(1\)

\(B=\left(\frac{1}{2}\right)^{2015}.\left(\frac{2}{3}\right)^{2016}.\left(-3\right)^{2015}\)

\(B=\left(-3\right)^{2015}.\left(\frac{2}{3}\right)^{2016}.\frac{1}{2^{2015}}\)

\(B=\left(-3\right)^{2015}.\frac{1}{2^{2015}}.\frac{2^{2016}}{3^{2016}}\)

\(B=\left(-3^{2015}\right).\frac{1}{2^{2015}}.\frac{2^{2016}}{3^{2016}}\)

\(B=-\frac{1}{2^{2015}}.\frac{2^{2016}}{3^{2016}}.3^{2015}\)

\(B=-\frac{1.2^{2016}.3^{2015}}{2^{2015}.3^{2016}}\)

\(B=-\frac{2^{2016}.3^{2015}}{3^{2016}.2^{2015}}\)

\(B=\frac{3^{2015}.2}{3^{2016}}\)

\(B=-\frac{2}{3}\)

Đề bài của bạn ​SAI rồi.

\(B=\dfrac{-1}{9}+\dfrac{8}{7}+\dfrac{10}{9}+\dfrac{-29}{7}\\ B=\left(\dfrac{-1}{9}+\dfrac{10}{9}\right)+\left(\dfrac{8}{7}+\dfrac{-29}{7}\right)\\ B=1+\dfrac{-11}{7}=1\dfrac{-11}{7}\)

B=\(-\dfrac{1}{9}+\dfrac{8}{7}+\dfrac{10}{9}+\dfrac{-29}{7}\)

\(B=\left(-\dfrac{1}{9} +\dfrac{10}{9}\right)+\left(\dfrac{8}{7}-\dfrac{29}{7}\right)\)

\(B=1+\left(-3\right)\)

\(B=-2\)

A = 1-3 + .........+ 97-98 + 101 

=  ( -2) +.......+(-2) + 101 

= (-2) x98 + 101 

= -196 + 101 

= -95

Tính hợp lí:

b) 42. 3 - 7 . [(-34) + 18]

= 7. 6. 3 – 7. [(-34) + 18]

= 7. 18 – 7. [(-34) + 18] 

= 7. [18 - (- 34) – 18]

= 7. [(18 – 18) + 34]

= 7. (0 + 34)

= 7. 34

= 238.

\(a,1-2+3-4+5-6+......+199-200\)

\(=\left(1-2\right)+\left(3-4\right)+\left(5-6\right)+.....+\left(199-200\right)\)( 100 cặp )

\(=-1+\left(-1\right)+\left(-1\right)+........+\left(-1\right)\)( 100 số hạng )

\(=-1.100\)

\(=-100\)

\(a.1-2+3-4+5-6+...+199-200\)

\(=\left(1-2\right)+\left(3-4\right)+\left(5-6\right)+...+\left(199-200\right)\)  (có tất cả \(200:2=100\)cặp)

\(=\left(-1\right)+\left(-1\right)+\left(-1\right)+...+\left(-1\right)\)

\(=\left(-1\right).200=-200\)

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

\(=\left(1+2-3-4\right)+\left(5+6-7-8\right)+...+\left(97+98-99-100\right)\)  (có \(100:4=25\)cặp)

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

\(=\left(-4\right).25=-100\)

\(c.1+\left(-6\right)+11+\left(-16\right)+...+21+\left(-26\right)\)

\(=\left[1+\left(-6\right)\right]+\left[11+\left(-16\right)\right]+...+\left[21+\left(-26\right)\right]\) (có tất cả \(26:2=13\)cặp)

\(=\left(-5\right)+\left(-5\right)+...+\left(-5\right)\)

\(=-5.13=-65\)

996 + 45 = 996 + (4 + 41) = (996 + 4) + 41 = 1000 + 41 = 1041

37 + 198 = (35 + 2) + 198 = (198 + 2) + 35 = 200 + 35 = 235

\(B=-\left(1+4+7+...+100\right)\\ B=-\dfrac{\left(100+1\right)\left[\left(100-1\right):3+1\right]}{2}=-\dfrac{101\cdot34}{2}=-1717\\ C=10+10+10+10-103=50-103=-53\)

Bạn có thể viết rõ ra ko chứ ntn tớ ko nhìn được