Question

\(y=\frac{1}{1.2.3.4}+\frac{1}{2.3.4.5}+...+\frac{1}{27.28.29.30}\)

Answer 1

Giải tiếp(ko chép đề)

= 1/1 - 1/2 - 1/3 - 1/4 + 1/2 - 1/3 - 1/4 - 1/5 + ... + 1/27 - 1/28 - 1/29 - 1/30

= 1 - 1/30

= 29/30

ks nha 

Answer 2

Bài giải :(không chép đề)

=1-1/2-1/3-1/4-1/5+1/2-1/3-1/4-1/5+........+1/27-1/28-1/29-1/30

=1-1/30

=29/30

Vậy số cần tìm là:29/30 Suy ra Y=29/30

Answer 3

\(\frac{1}{1.2.3.4}=\frac{1}{3}\left(\frac{1}{1.2.3}-\frac{1}{2.3.4}\right)\)
\(\frac{1}{2.3.4.5}=\frac{1}{3}\left(\frac{1}{2.3.4}-\frac{1}{3.4.5}\right)\)
.........
\(\frac{1}{27.28.29.30}=\frac{1}{3}\left(\frac{1}{27.28.29}-\frac{1}{28.29.30}\right)\)
\(y=\frac{1}{3}\left(\frac{1}{1.2.3}-\frac{1}{2.3.4}\right)+\frac{1}{3}\left(\frac{1}{2.3.4}-\frac{1}{3.4.5}\right)+...+\frac{1}{3}\left(\frac{1}{27.28.29}-\frac{1}{28.29.30}\right)\)
\(y=\frac{1}{3}\left(\frac{1}{1.2.3}-\frac{1}{2.3.4}+\frac{1}{2.3.4}-\frac{1}{3.4.5}+...+\frac{1}{27.28.29}-\frac{1}{28.29.30}\right)\)
\(y=\frac{1}{3}\left(\frac{1}{1.2.3}-\frac{1}{28.29.30}\right)\)
CÒN LẠI TỰ LÀM NỐT, MỎI TAY QUÁ RÙI =))

Answer 4

CÁCH 2 =)) 
\(3y=\frac{3}{1.2.3.4}+\frac{3}{2.3.4.5}+...+\frac{3}{27.28.29.30}\)
\(3y=\frac{1}{1.2.3}-\frac{1}{2.3.4}+\frac{1}{2.3.4}-\frac{1}{3.4.5}+...+\frac{1}{27.28.29}-\frac{1}{28.29.30}\)
\(3y=\frac{1}{1.2.3}-\frac{1}{28.29.30}\)
\(y=\left(\frac{1}{1.2.3}-\frac{1}{28.29.30}\right)\div3\)
\(y=\left(\frac{1}{1.2.3}-\frac{1}{28.29.30}\right)\times\frac{1}{3}\)
CÒN LẠI TỰ TÍNH,MỎI TAY QUÁ RÙI =))