I don't know

\(\frac{2}{3}+\frac{2}{15}+\frac{2}{35}+...+\frac{2}{9999}\)

\(=\frac{2}{1\times3}+\frac{2}{3\times5}+\frac{2}{5\times7}+...+\frac{2}{99\times101}\)

\(=\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{99}-\frac{1}{101}\)

\(=\frac{1}{1}-\frac{1}{101}=\frac{101}{101}-\frac{1}{101}=\frac{100}{101}\)

\(\frac{2}{3}+\frac{2}{15}+\frac{2}{35}+...+\frac{2}{9999}\)

\(=\frac{2}{1.3}+\frac{2}{3.5}+\frac{1}{5.7}+....+\frac{2}{99.101}\)

\(=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{99}-\frac{1}{101}\)

\(=1-\frac{1}{101}+0+0+...+0\)

\(=\frac{100}{101}\)

1/101

biến đổi ra là đc

\(1-\left(\frac{2}{3}+\frac{2}{3.5}+\frac{2}{5.7}+..+\frac{2}{99.101}\right)\)

tới đây thôi bạn tự làm đi

\(C=1-\frac{2}{3}+\frac{2}{15}+\frac{2}{35}+...+\frac{2}{9999}\)

\(C=1-\frac{2}{1x3}+\frac{2}{3x5}+\frac{2}{5x7}+\frac{2}{99x101}\)

\(C=1-\left(\frac{2}{1}-\frac{2}{3}+\frac{2}{3}-\frac{2}{5}+\frac{2}{5}-\frac{2}{7}+...\frac{2}{99}-\frac{2}{101}\right)\)

\(C=1-\left(\frac{2}{1}-\frac{2}{101}\right)\)

\(C=1-\frac{200}{101}\)\(=\frac{1}{1}-\frac{200}{101}=\frac{101}{101}-\frac{200}{101}=\frac{-99}{0}\)

\(-2\left(\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+\frac{1}{99}+...+\frac{1}{9999}\right)\)

\(=-2\left(\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}+\frac{1}{99.101}\right)\)\(=-2\cdot\left(\frac{1}{3}-\frac{1}{101}\right)\)

=.....

mình quên đem máy tính nên k ghi đc đấp số

THÔNG CẢM

-.(2/3.5+2/5.7+...+

-2/3.5+(-2/5.7)+(-2/7.9)+(-2/9.11)+.....+(-2/99.111)

2/3+2/15+2/35+2/63+...+2/9999

=2/1.3+2/3.5+2/5.7+...+2/99x101

=1-1/3+1/3-1/5+...+1/99-1/101

=1-1/101=100/101

\(=2\times\left(\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+...+\frac{1}{9999}\right)\)

\(=2\times\left(\frac{1}{1\times3}+\frac{1}{3\times5}+\frac{1}{5\times7}+...+\frac{1}{99\times101}\right)\)

\(=2\times\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{99}-\frac{1}{101}\right)\)

\(=2\times\left(\frac{1}{1}-\frac{1}{101}\right)\)

\(=2\times\frac{100}{101}\)

\(=\frac{200}{101}\)

\(\frac{2}{3}+\frac{2}{15}+\frac{2}{35}+.....+\frac{2}{9999}\)

\(=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+.......+\frac{2}{99.101}\)

\(=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{99}-\frac{1}{101}\)

\(=1-\frac{1}{101}=\frac{100}{101}\)

a) 1+2+3+...+99+100

giải

Từ 1 đến 100  có 100 số.Như vậy,số cặp số là:

100:2=50(cặp)

Mỗi cặp số có tổng bằng:

1+100(2+99)(3+98)...=11

Kết quả của phép tính là:

101x50=5050

Đáp số:5050

1+2+...+100=(1+100).100/2=5150

a)5050

b)325

c)Nguyễn Văn Chịu

Giải:

\(\dfrac{2}{3}+\dfrac{2}{15}+\dfrac{2}{35}+\dfrac{2}{63}+\dfrac{2}{99}+\dfrac{2}{143}\) 

\(=\dfrac{2}{1.3}+\dfrac{2}{3.5}+\dfrac{2}{5.7}+\dfrac{2}{7.9}+\dfrac{2}{9.11}+\dfrac{2}{11.13}\) 

\(=\dfrac{1}{1}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{13}\) 

\(=\dfrac{1}{1}-\dfrac{1}{13}\) 

\(=\dfrac{12}{13}\) 

Chúc em học tốt!

2/3+2/15+2/35+2/63+2/99+2/143

=2(1/1x3+1/3x5+1/5x7+1/7x9+1/9x11+1/11x13)

=2(1-1/3+1/3-1/5+1/5-....+1/13)

=2(1-1/13)

=2.12/13=24/13