Question

 Tính tổng sau bằng cách nhanh nhất.

a) 1/2 + 1/6 + 1/12 + 1/20 + 1/30 + 1/42 + 1/56

b) 17/9 + 19/3 + 14/6 + 7/13 + 10/6 + 1/9

Answer 1

= 1/1x2+1/2x3+...+1/7x8

= 1-1/2+1/2-...-1/8

= 1-1/8

=7/8

Answer 2

a/ \(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}=\)

\(=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}=\)

= 1-1/8 = 7/8

b/ = (17/9+1/9)+(19/13+7/13)+(14/6+10/6) = 18/9 + 26/13 + 24/6 = 2+2+4 = 8

Answer 3

\(a)\) \(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}\)

\(=\)\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}\)

\(=\)\(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}\)

\(=\)\(1-\frac{1}{8}\)

\(=\)\(\frac{7}{8}\)

Áp dụng công thức \(\frac{a}{b\left(b+a\right)}=\frac{1}{b}-\frac{1}{b+a}\) \(\left(a,b>0\right)\) nhé 

Chúc bạn học tốt ~