3x/4 + 3x/28 + 3x/70 + ... + 3x/304 = 18/19
=> x(3/1*4 + 3/4*7 + 3/7*10 + ... + 3/16*19) = 18/19
=> x(1 - 1/4 + 1/4 - 1/7 + 1/7 - 1/10 + ... + 1/16 - 1/19) = 18/19
=> x(1 - 1/19) = 18/19
=> x*18/19 = 18/19
=> x = 1
\(3.\frac{x}{4}+3.\frac{x}{28}+3.\frac{x}{70}+...+3.\frac{x}{304}=\frac{18}{19}\)
\(3.\left(\frac{x}{4}+\frac{x}{28}+\frac{x}{70}+...+\frac{x}{304}\right)\)
\(\frac{x}{4}+\frac{x}{28}+\frac{x}{70}+...+\frac{x}{304}=\frac{18}{19}:3=\frac{6}{19}\)
Nhân hai vế với 3/x ta được
\(\frac{3}{x}\left(\frac{x}{4}+\frac{x}{28}+\frac{x}{70}+...+\frac{x}{304}\right)=\frac{6}{19}.\frac{3}{x}\)
\(\frac{3}{x}.\frac{x}{4}+\frac{3}{x}.\frac{x}{28}+\frac{3}{x}.\frac{x}{70}+...+\frac{3}{x}.\frac{x}{304}=\frac{18}{19.x}\)
\(\frac{3}{4}+\frac{3}{28}+\frac{3}{70}+...+\frac{3}{304}=\frac{18}{19}:x\)
\(\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+...+\frac{3}{16.19}=\frac{18}{19}:x\)
\(1-\frac{1}{19}=\frac{18}{19}:x\)
\(\frac{18}{19}=\frac{18}{19}:x\)
\(x=\frac{18}{19}:\frac{18}{19}=1\)
Chúc bạn học tốt !!!
P/s: Không hiểu chỗ nào cứ ib
