Số số hạng dãy số là :

(355-1):2+1=178

Tổng B là :

(1+355)x178:2=31684

Vậy B=31684

Đáp số:31684

Có số số hạng là:

(355 - 1) : 2 + 1 = 178

Tổng B là :

(1 + 355) x 178 : 2 = 31684

Đáp số: 31684

4: \(=\dfrac{2+3}{7}+\dfrac{1+6}{9}-\dfrac{5}{6}=\dfrac{5}{7}+\dfrac{7}{9}-\dfrac{5}{6}=\dfrac{83}{126}\)

5: \(=\dfrac{-5-2}{7}+\dfrac{3+1}{4}-\dfrac{1}{5}=-\dfrac{1}{5}\)

6: \(=\dfrac{-3-28}{31}+\dfrac{-6-1}{17}+\dfrac{1-5}{25}=-1-\dfrac{7}{17}-\dfrac{4}{25}=-\dfrac{668}{425}\)

4. \(\dfrac{2}{7}+\dfrac{1}{9}+\dfrac{3}{7}+\dfrac{5}{9}+\dfrac{-5}{6}\)

\(=\left(\dfrac{2}{7}+\dfrac{3}{7}\right)+\left(\dfrac{1}{9}+\dfrac{5}{9}\right)+\dfrac{-5}{6}\)

\(=\dfrac{5}{7}+\dfrac{2}{3}+\dfrac{-5}{6}\)

\(=\dfrac{30+28+\left(-35\right)}{42}=\dfrac{23}{42}\)
 

5. \(\dfrac{-5}{7}+\dfrac{3}{4}+\dfrac{-1}{5}+\dfrac{-2}{7}+\dfrac{1}{4}\)

\(=\left(\dfrac{-5}{7}+\dfrac{-2}{7}\right)+\left(\dfrac{3}{4}+\dfrac{1}{4}\right)+\dfrac{-1}{5}\)

\(=\dfrac{-7}{7}+\dfrac{4}{4}+\dfrac{-1}{5}\)

\(=-1+1+\dfrac{-1}{5}\)

\(=-\dfrac{1}{5}\)
 

6. \(\dfrac{-3}{31}+\dfrac{-6}{17}+\dfrac{1}{25}+\dfrac{-28}{31}+\dfrac{-1}{17}+\dfrac{-1}{5}\)

\(=\left(\dfrac{-3}{31}+\dfrac{-28}{31}\right)+\left(\dfrac{-6}{17}+\dfrac{-1}{17}\right)+\dfrac{1}{25}+\dfrac{-1}{5}\)

\(=\dfrac{-31}{31}+\dfrac{-7}{17}+\dfrac{1}{25}+\dfrac{-1}{5}\)

\(=-1+\dfrac{-7}{17}+\dfrac{1}{25}+\dfrac{-1}{5}\)

\(=\dfrac{-425+\left(-175\right)+17+\left(-85\right)}{425}=\dfrac{-668}{425}\)

Quy luật đơn giản thôi

a, 4 + 4 + 8 + 12 +20 +.. +576 

ST3 =ST2 +St1

St 4 = st 3 +st2

......

b, St4 =st3 +st2 +st1

  st5 = st4 + st3 +st2 

......

I don't know how fast it is. I just know how to calculate slowly

số số hạng là :

`(361 - 1) :6 + 1 = 61 ( số hạng)`

`61 : 2 = 30 (dư 1 nhóm)`

`(1-7) + (13 - 19) + ... +(349 -355) + 361`

`= (-6) + (-6) + ... + -6 + 361`

`= (-6).30  + 361`

`=-180 + 361`

`= 181`

=(1-7)+(13-19)+(25-31)+...+(349-355)+361

=361-6*30

=361-180=181

\(\dfrac{17}{5}.\dfrac{-31}{125}.\dfrac{1}{2}.\dfrac{10}{17}.\dfrac{-1}{2^3}\\= \left(\dfrac{17}{5}.\dfrac{10}{17}\right)\left(\dfrac{-31}{125}.\dfrac{-1}{8}\right).\dfrac{1}{2}\\ =2.\dfrac{31}{1000}.\dfrac{1}{2}\\ =\left(2.\dfrac{1}{2}\right).\dfrac{31}{1000}\\ =1.\dfrac{31}{1000}\\ =\dfrac{31}{1000}\)

Bài 1: Ta chỉ cần bỏ ngoặc rồi cộng hai phân số để ra kết quả là số tự nhiên là xong

Bài 2:

A = \(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+............+\frac{1}{2003.2004}\)

A = \(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-.............-\frac{1}{2003}+\frac{1}{2003}-\frac{1}{2004}\)

A = \(1-\frac{1}{2004}\)

A = \(\frac{2004}{2004}-\frac{1}{2004}=\frac{2003}{2004}\)

Mk làm mẫu 1 bài nha 

Bài 1 :

a, = (1/4+3/4) - (5/13+8/13)+2/11

    = 1 - 1 + 2/11

    = 2/11

Tk mk nha

\(A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2003.2004}\)

\(\Leftrightarrow A=1\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2003}-\frac{1}{2004}\right)\)

\(\Leftrightarrow A=1\left(1-\frac{1}{2004}\right)\)

\(\Leftrightarrow A=\frac{2003}{2004}\)