Question

Tính tỏng\(B=\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+...+\frac{1}{37.38.39}\)

\(A=\frac{1}{41}+\frac{1}{42}+...+\frac{1}{80}\) so sánh a với \(\frac{7}{42}\)

Answer 1

\(2B=\frac{2}{1\cdot2\cdot3}+\frac{2}{2\cdot3\cdot4}+\frac{2}{3\cdot4\cdot5}+..+\frac{2}{37\cdot38\cdot39}\)

\(2B=\frac{1}{1\cdot2}-\frac{1}{2\cdot3}+\frac{1}{2\cdot3}-\frac{1}{3\cdot4}+\frac{1}{3\cdot4}-\frac{1}{4\cdot5}+..+\frac{1}{37\cdot38}-\frac{1}{38\cdot39}\)

\(2B=\frac{1}{2}-\frac{1}{1482}\)

\(B=\frac{185}{741}\)

Answer 2

\(A>\frac{1}{80}+\frac{1}{80}+..+\frac{1}{80}\)

\(A>\frac{1}{80}\cdot40>\frac{7}{42}\)

\(A>\frac{7}{42}\)