1/12 + 1/20 + ... + 1/132
= 1/3×4 + 1/4×5 + ... + 1/11×12
= 1/3 - 1/4 + 1/4 - 1/5 + ... + 1/11 - 1/12
= 1/3 - 1/12
= 4/12 - 1/12
= 3/12 = 1/4
\(=\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+...+\frac{1}{11.12}\)
\(=\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{11}-\frac{1}{12}\)
\(=\frac{1}{3}-\frac{1}{12}\)
\(=\frac{1}{4}\)
1/12 + 1/20 + ... + 1/132
= 1/3.4 + 1/4.5 + 1/6.7 + 1/7.8 + 1/9.10 + 1/10.11 + 1/11.12
= 1/3 - 1/4 + 1/4 - 1/5 + 1/6 - 1/7 + 1/7 - 1/8 + 1/9 - 1/10 + 1/10 - 1/11 + 1/11 - 1/12
= 1/3 - 11/30 - 17/72 - 1/12
= \(-\left(\frac{127}{360}\right)\)
= 1/3.4 + 1/4.5 + 1/5.6 + ... + 1/ 11.12
= 1/3 . 1/4 + 1/4 . 1/5 + 1/5 . 1/6 + ... + 1/11 - 1/12
= 1/3 - 1/12
=1/4
1/3.4 + 1/4.5 + 1/6.7 + 1/7.8 + 1/8.9 + 1/9.10 + 1/10.11 + 1/11.12
=1/3 - 1/4 + 1/4 - 1/5 + 1/6 - 1/7 + 1/7 - 1/8 + 1/8 - 1/9 + 1/9 - 1/10 + 1/10 - 1/11 + 1/11 - 1/12
=1/3 - 1/12
=1/3 + (-1/12)
1/4
Tiếc chi =)
1/12+1/20+1/42+1/56+1/72+1/90+1/110+1/132
=1/3x4+1/4x5+1/6x7+1/7x8+1/8x9+1/9x10
=...............(còn lại bạn tinh nhà)