\(\left(\dfrac{1}{2}+1\right)\times\left(\dfrac{1}{3}+1\right)\times\left(\dfrac{1}{4}+1\right)\times\left(\dfrac{1}{5}+1\right)\times\left(\dfrac{1}{6}+1\right)\)
\(=\dfrac{3}{2}\times\dfrac{4}{3}\times\dfrac{5}{4}\times\dfrac{6}{5}\times\dfrac{7}{6}\)
\(=\dfrac{3\times4\times5\times6\times7}{2\times3\times4\times5\times6}\)
\(=\dfrac{7}{2}\)
(
2
1
+1)×(
3
1
+1)×(
4
1
+1)×(
5
1
+1)×(
6
1
+1)
=
3
2
×
4
3
×
5
4
×
6
5
×
7
6
=
2
3
×
3
4
×
4
5
×
5
6
×
6
7
=
3
×
4
×
5
×
6
×
7
2
×
3
×
4
×
5
×
6
=
2×3×4×5×6
3×4×5×6×7
=
7
2
=
2
7