Số số hạng của tổng trên là:
      (1000 - 1) : 1 + 1 = 1000(số)

Tổng trên có giá trị là:

         (1000 + 1) x 1000 : 2 = 500500

500500

1+2+3+4+5+6+7+8+................+999+1000

     (1000-1):1+1

=________________ x(1000+1)

               2

=500500

(1+2)+[(-3)+(-4)]+...+[(-999)+(-1000)]

=3-7+11-...-1999

=(3-7)+(11-15)+...+(1995-1999)

=-4+(-4)+...+(-4)

=-4.250

=-1000

500500 dung 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000%

Ta có:

\(\dfrac{1}{2}< 1;\dfrac{3}{4}< 1;\dfrac{5}{6}< 1;...;\dfrac{999}{1000}< 1\)

\(\Rightarrow\dfrac{1}{2}.\dfrac{3}{4}.\dfrac{5}{6}...\dfrac{999}{1000}< 1\)

\(\Rightarrow p< 1\)

câu nay tôi viết sai là p, các nhớ sửa thành a nhé

\(B=\frac{\frac{2016}{1000}+\frac{2016}{999}+...+\frac{2016}{501}}{\frac{-1}{1.2}+\frac{-1}{3.4}+...+\frac{-1}{999.1000}}=\frac{2016.\left(\frac{1}{1000}+\frac{1}{999}+...+\frac{1}{501}\right)}{-\left(\frac{1}{1.2}+\frac{1}{3.4}+...+\frac{1}{999.1000}\right)}\)

\(=\frac{2016.\left(\frac{1}{1000}+\frac{1}{999}+...+\frac{1}{501}\right)}{-\left(1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{999}-\frac{1}{1000}\right)}\)

\(=\frac{2016\left(\frac{1}{1000}+\frac{1}{999}+...+\frac{1}{501}\right)}{-\left[\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{999}+\frac{1}{1000}\right)-2\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+...+\frac{1}{1000}\right)\right]}\)

\(=\frac{2016.\left(\frac{1}{1000}+\frac{1}{999}+...+\frac{1}{501}\right)}{-\left[\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{999}+\frac{1}{1000}\right)-\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{500}\right)\right]}\)

\(=\frac{2016.\left(\frac{1}{1000}+\frac{1}{999}+...+\frac{1}{501}\right)}{-\left(\frac{1}{501}+\frac{1}{502}+\frac{1}{503}+....+\frac{1}{999}+\frac{1}{1000}\right)}=\frac{2016}{-1}=-2016\)

Vậy B = - 2016

Bạn Xyz cho mik hỏi ở phần mẫu số tại sao lại có -2*(1/2+1/4+...+1/1000) vậy? Nó ở đâu ra thế?

\(\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+...+\frac{1}{999\times1000}+1\)

\(=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+....+\frac{1}{999000}+1\)

\(=1-\frac{1}{1000}+1\)

\(=\frac{1999}{1000}\)

bằng 1999/1000

B=(2+4+6+...+1000)—(1+3+5+...+999)

B=(2—1)+(4—3)+(6—5)+....+(1000—999)

B=1+1+1+....+1

B=1x500

B=500

B=2+4+6+...+1000-1-3-5-...-999

B=(2-1)+(4-3)+...+(1000-999)

B=1+1+...+1 (500 số 1)

B=1x500

B=500

Vậy B=500 nhé

B = 2 + 4 + 6 + ... + 1000 - 1 - 3 - 5 - ... - 999

B = ( 2 - 1 ) + ( 4 - 3 ) + ... + ( 1000 - 999 )

B = 1 + 1 + ... + 1 ( 500 số1 )

B = 1 x 500

B = 500