Question

[bò sữa]

tính nhanh:A=1/2+1/6+1/12+1/20+...+1/132

Answer 1

[Nguyễn Minh Đức]

\(A=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{132}\)

\(=\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+...+\frac{1}{11\cdot12}\)

\(=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{11}-\frac{1}{12}\)

\(=1-\frac{1}{12}=\frac{11}{12}\)

Vậy \(A=\frac{11}{12}\)

Chúc bạn học tốt ^^!!!

Answer 2

[Ngọc Lan]

\(A=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{132}\)

\(=\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+...+\frac{1}{11\times12}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{11}-\frac{1}{12}\)

\(=1-\frac{1}{12}=\frac{11}{12}\)

Chúc bạn học tốt!

#Huyền#