\(\dfrac{1}{1.4}+\dfrac{1}{4.7}+...+\dfrac{1}{34.37}+\dfrac{1}{37.40}\)

\(=1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+...+\dfrac{1}{34}-\dfrac{1}{37}+\dfrac{1}{37}-\dfrac{1}{40}\)

\(=1-\dfrac{1}{40}\)

\(=\dfrac{39}{40}\)

1/(1×4) + 1/(4×7) + ... + 1/(34×37) + 1/(37×40)

= 1/3 × (1 - 1/4 + 1/4 - 1/7 + ... + 1/34 - 1/37 + 1/37 - 1/40)

= 1/3 × (1 - 1/40)

= 1/3 × 39/40

= 13/40

\(\dfrac{1}{1.4}+\dfrac{1}{4.7}+...+\dfrac{1}{34.37}+\dfrac{1}{37.40}\)

\(=1-\left(\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+...+\dfrac{1}{34}-\dfrac{1}{37}+\dfrac{1}{37}-\dfrac{1}{40}\right)\)

\(=1-\dfrac{1}{40}\)

\(=\dfrac{39}{40}\)

Vậy giá trị cần tìm là: \(\dfrac{39}{40}\)

\(3xA=\dfrac{4-1}{1x4}+\dfrac{7-4}{4x7}+...+\dfrac{37-34}{34x37}+\dfrac{40-37}{37x40}=\)

\(=1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{17}{ }+...+\dfrac{1}{34}-\dfrac{1}{37}+\dfrac{1}{37}-\dfrac{1}{40}=\)

\(=1-\dfrac{1}{40}=\dfrac{39}{40}\Rightarrow A=\dfrac{39}{40}:3=\dfrac{13}{40}\)

\(=\dfrac{1}{3}\left(\dfrac{3}{1.4}+\dfrac{3}{4.7}+...+\dfrac{3}{34.37}+\dfrac{3}{37.40}\right)\)

\(=\dfrac{1}{3}\left(1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+...+\dfrac{1}{34}-\dfrac{1}{37}+\dfrac{1}{37}-\dfrac{1}{40}\right)\)

\(=\dfrac{1}{3}.\dfrac{39}{40}\)

\(=\dfrac{13}{40}\)

Ta có    1/1x4+1/4x7+...+1/2002x2005

  <=>   =1/3.3(1/1x4+1/4x7+...+1/2002x2005)

            =1/3(3/1x4+3/4x7+...+3/2002x2005)

            =1/3(1-1/4+1/4-1/7+...+1/2002-1/2005)

            =1/3(1-1/2005)

            =1/3.2004/2005

            =1.2004/3.2005

            =668/2005

\(\frac{1}{1.4}\)+ \(\frac{1}{4.7}\)+...+\(\frac{1}{2002.2005}\)=3(\(\frac{1}{1.4}\)+ \(\frac{1}{4.7}\)+...+ \(\frac{1}{2002.2005}\)):3=(\(\frac{3}{1.4}\)+ \(\frac{3}{4.7}\)+...+ \(\frac{3}{2002.2005}\)):3= (1-\(\frac{1}{4}\)+ \(\frac{1}{4}\)- \(\frac{1}{7}+...+\frac{1}{2002}-\frac{1}{2005}\)):3=(1-\(\frac{1}{2005}\)) : 3 = \(\frac{668}{2005}\)

= \(\frac{1}{3}\left(\frac{1}{1}-\frac{1}{4}+\frac{1}{4}-.....+\frac{1}{x}-\frac{1}{x+1}\right)\) ) 

= \(\frac{1}{3}\left(1-\frac{1}{x+1}\right)\)

=\(\frac{1}{3}x\left(\frac{x+1}{x+1}-\frac{1}{x+1}\right)\)

= \(\frac{1}{3}x\frac{x}{x+1}\)

dè bài la tim x

Tong cua phep. Tinh la 2009/6030

Ta có :

1/1.4+1/4.7+...+1/91.94

=1/3.(1/1-1/4+...+1/91-1/94)

=1/3.(1/1-1/94)

=1/3.93/94

=31/94

Ta có :

1/1.4+1/4.7+...+1/91.94

=1/3.(1/1-1/4+...+1/91-1/94)

=1/3.(1/1-1/94)

=1/3.93/94

=31/94

Ta có :

1/1.4+1/4.7+...+1/91.94

=1/3.(1/1-1/4+...+1/91-1/94)

=1/3.(1/1-1/94)

=1/3.93/94

=31/94

Giờ anh đang bận hồi nữa anh giúp cho nha

\(F=\dfrac{1}{x}\left(\dfrac{1}{1.4}+\dfrac{1}{4.7}+...+\dfrac{1}{97.100}+\dfrac{1}{100.103}\right)\)

\(3F=\dfrac{1}{x}\left(\dfrac{3}{1.4}+\dfrac{3}{4.7}+...+\dfrac{3}{97.100}+\dfrac{3}{100.103}\right)\)

\(F=\dfrac{\dfrac{1}{x}\left(\dfrac{1}{3}-\dfrac{1}{103}\right)}{3}=\dfrac{\dfrac{1}{x}.\dfrac{100}{309}}{3}=\dfrac{\dfrac{100x}{309}}{3}=\dfrac{100x}{927}\)

\(F=\dfrac{1}{3}\cdot\left(1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+...+\dfrac{1}{100}-\dfrac{1}{103}\right)\)

\(=\dfrac{1}{3}\left(1-\dfrac{1}{103}\right)=\dfrac{1}{3}.\dfrac{102}{103}=\dfrac{204}{309}\)

mà mình không phải là Thiên Tỷ mình tên là Gia Yến đấy nhé

\(F=\dfrac{1}{3}\left(\dfrac{3}{1\cdot4}+\dfrac{3}{4\cdot7}+...+\dfrac{3}{100\cdot103}\right)\)

\(=\dfrac{1}{3}\left(1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+...+\dfrac{1}{100}-\dfrac{1}{103}\right)\)

\(=\dfrac{1}{3}\cdot\dfrac{102}{103}=\dfrac{34}{103}\)

tinh nhanh 1/1x4 + 1/4x7 +1/7x10 +...+ 1/91x94 

Ta có :

1/1.4+1/4.7+...+1/91.94

=1/3.(1/1-1/4+...+1/91-1/94)

=1/3.(1/1-1/94)

=1/3.93/94

=31/94