Question

15/1*2+15/2*3+15/3*4+ . . . +15/19*20

Answer 1

Đặt tổng trên = A

\(A=\frac{15}{1.2}+\frac{15}{2.3}+\frac{15}{3.4}+...+\frac{15}{19.20}\)

\(A:15=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{19.20}\)

\(A:15=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{19}-\frac{1}{20}\)

\(A:15=1-\frac{1}{20}=\frac{19}{20}\)

\(A=\frac{19}{20}.15=\frac{57}{4}\)

Answer 2

\(A=\frac{15}{1.2}+\frac{15}{2.3}+\frac{15}{3.4}+...+\frac{15}{19.20}\)

\(A:15=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{19.20}\)

\(A:15=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{19}-\frac{1}{20}\)

\(A:15=1-\frac{1}{20}=\frac{19}{20}\)

\(A=\frac{19}{20}.15=\frac{57}{4}\)