Chứng minh rằng :

1 - \(\frac{1}{2}\)+\(\frac{1}{3}\) - \(\frac{1}{4}\) + \(\frac{1}{5}\) - \(\frac{1}{6}\)+ . . . + \(\frac{1}{999}\)-\(\frac{1}{1000}\) = \(\frac{1}{501}\)+ \(\frac{1}{502}\)+\(\frac{1}{503}\) + . . . + \(\frac{1}{1000}\)

Chứng minh rằng :

1 - \(\frac{1}{2}\)+ \(\frac{1}{3}\)-\(\frac{1}{4}\)+ \(\frac{1}{5}\)- \(\frac{1}{6}\)+ . . . + \(\frac{1}{999}\)- \(\frac{1}{1000}\)= \(\frac{1}{501}\)+ \(\frac{1}{502}\)+\(\frac{1}{503}\)+ . . . + \(\frac{1}{1000}\)

tính :

\(\frac{2}{3}\)+\(\frac{1}{3}\)

\(\frac{3}{4}\)+\(\frac{2}{4}\)+\(\frac{1}{4}\)

\(\frac{4}{5}\)+\(\frac{3}{5}\)+\(\frac{2}{5}\)+\(\frac{1}{5}\)

\(\frac{5}{6}\)+\(\frac{4}{6}\)+\(\frac{3}{6}\)+\(\frac{2}{6}\)+\(\frac{1}{6}\)

từ các kết quả trên , hãy tính giá trị của tổng dưới đây

\(\frac{999}{1000}\)+\(\frac{998}{1000}\)+\(\frac{997}{1000}\)+ ... +\(\frac{1}{1000}\)

giúp mình nha mình cần gấp lắm , cảm ơn

Câu 1 : Tính

a) \(\frac{2}{3}\)+\(\frac{1}{3}\)x ( \(\frac{-4}{9}\)+\(\frac{5}{6}\)) : \(\frac{7}{12}\)

b) S = \(\frac{1}{2}\)x \(\frac{1}{3}\)+\(\frac{1}{3}\)x\(\frac{1}{4}\)+\(\frac{1}{4}\)x\(\frac{1}{5}\)+\(\frac{1}{5}\)x\(\frac{1}{6}\)+\(\frac{1}{6}\)x\(\frac{1}{7}\)+\(\frac{1}{7}\)x\(\frac{1}{8}\)+\(\frac{1}{8}\)x\(\frac{1}{9}\)

c) A = \(\frac{5}{5.7}\)+\(\frac{5}{7.9}\)+...+\(\frac{5}{59.61}\)

d) M = \(\frac{3}{4}\)x\(\frac{8}{9}\)x\(\frac{15}{16}\)x\(\frac{24}{25}\)x...x\(\frac{99}{100}\)

e) N = \(\frac{1}{2}\)x\(\frac{-2}{3}\)x\(\frac{3}{4}\)x\(\frac{-4}{5}\)x\(\frac{5}{6}\)x\(\frac{-6}{7}\)x...x\(\frac{-98}{99}\)x\(\frac{99}{100}\)

[ Các bạn trả lời cách tính nhanh mà đúng nhá :)) ]

[ Cảm ơn các bạn nhiều <3 ]

a) A =(1-\(\frac{1}{2}\))x( 1-\(\frac{1}{3}\))x(1-\(\frac{1}{4}\))x ..... x(1-\(\frac{1}{2017}\))

b) B =5\(\frac{9}{10}\):\(\frac{3}{2}\)-(2\(\frac{1}{3}\)x 4\(\frac{1}{2}\)-2x2\(\frac{1}{3}\)):\(\frac{7}{4}\)

Bài 1:  \(\frac{1}{6}\)+\(\frac{-5}{7}\): x    =   \(\frac{-7}{18}\)

Bài 2: Tìm tích

a)\(\left(\frac{1}{2}+1\right).\left(\frac{1}{3}+1\right).\left(\frac{1}{4}+1\right)...\left(\frac{1}{999}+1\right)\)

b)\(\left(\frac{1}{2}-1\right).\left(\frac{1}{3}-1\right).\left(\frac{1}{4}-1\right)...\left(\frac{1}{1000}-1\right)\)

c)\(\frac{3}{2^2}.\frac{8}{3^2}.\frac{15}{4^2}...\frac{99}{10^2}\)