Question

Tính tổng S = \(\frac{10}{56}+\frac{10}{140}+\frac{10}{260}+......+\frac{10}{1400}\)

Answer 1

S = 10/56 + 10/140 + 10/260 + ....... + 10/1400

S = 5/28 + 5/70 + 5/130 + 5/700

3S/5 = 3/4 x 7 + 3/7 x 10 + 30/10 x 13 + ....... + 3/25 x 28

3S/5 = 1/4 - 1/7 + 1/7 - 1/10 + 1/10 - 1/13 + ........ + 1/25 - 1/28

3S/5 = 1/4 - 1/28

3S/5 = 3/14

S = 3/14 x 5/3

S = 5/14

Vậy S = 5/14

Answer 2

\(S=\frac{10}{56}+\frac{10}{140}+\frac{10}{260}+\frac{10}{1400}\)

\(S=\frac{5}{28}+\frac{5}{70}+\frac{5}{130}+...+\frac{5}{700}\)

\(S=\frac{5}{4.7}+\frac{5}{7.10}+\frac{5}{10.13}+...+\frac{5}{25.28}\)

\(S=5.\left(\frac{3}{4.7}+\frac{3}{7.10}+\frac{3}{10.13}+...+\frac{3}{25.28}\right)\)

\(S=5.\left(\frac{1}{4.7}+\frac{1}{7.10}+\frac{1}{10.13}+...+\frac{1}{25.28}\right)\)

\(S=5.\left(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+...+\frac{1}{25}-\frac{1}{28}\right)\)

\(S=5.\left(\frac{1}{4}-\frac{1}{28}\right)\)

\(S=5.\frac{3}{14}=\frac{15}{14}\)

Vậy \(S=\frac{15}{14}\)

Answer 3

thank 2 bạn nha!

Answer 4

S = 10/56 + 10/140 + 10/260 + ....... + 10/1400 S = 5/28 + 5/70 + 5/130 + 5/700 3S/5 = 3/4 x 7 + 3/7 x 10 + 30/10 x 13 + ....... + 3/25 x 28 3S/5 = 1/4 ‐ 1/7 + 1/7 ‐ 1/10 + 1/10 ‐ 1/13 + ........ + 1/25 ‐ 1/28 3S/5 = 1/4 ‐ 1/28 3S/5 = 3/14 S = 3/14 x 5/3 S = 5/14 Vậy S = 5/14