Question

A = 1/ 3.7 + 1/ 7.11 +...+1/ 103. 107

Tính nhanh

Answer 1

\(A=\frac{1}{3.7}+\frac{1}{7.11}+...+\frac{1}{103.107}\)

\(A=\frac{1}{4}.\left(\frac{4}{3.7}+\frac{4}{7.11}+...+\frac{4}{103.107}\right)\)

\(A=\frac{1}{4}.\left(\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+...+\frac{1}{103}-\frac{1}{107}\right)\)

\(A=\frac{1}{4}.\left(\frac{1}{3}-\frac{1}{107}\right)\)

\(A=\frac{1}{4}.\frac{104}{321}\)

\(A=\frac{26}{321}\)

_Chúc bạn học tốt_

Answer 2

\(A=\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+...+\frac{1}{103}-\frac{1}{107}\)

\(A=\frac{1}{3}-\frac{1}{107}=\frac{104}{321}\)