Question

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

Tính tổng M

Answer 1

M=5/28+5/70+5/130+...+5/700.

M=5/4*7+5/7*10+5/10*13+...+5/25*58.

3/5*M=3/4*7+3/7*10+3/10*13+...+3/25*28.

3/5*M=1/4-1/28=3/14.

M=3/14:3/5=5/14.

Vậy M=5/14.

Answer 2

M=5/28+5/70+5/130+.....+5/700

M=1/5x(1/4x7+1/7x10+...+1/25x28)

M=1/5x(1/4-1/7+1/7-1/10+....+1./25-1/28)

M=1/5x(1/4-1/28)

M=1/5x3/14

M=3/70

Answer 3

\(M=\frac{5}{28}+\frac{5}{70}+\frac{5}{130}+...+\frac{5}{700}\)
\(M=5\left(\frac{1}{4.7}+\frac{1}{7.10}+\frac{1}{10.13}+...+\frac{1}{25.28}\right)\)
\(M=5\cdot\frac{1}{3}\left(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{25}-\frac{1}{28}\right)\)
\(M=\frac{5}{3}\left(\frac{1}{4}-\frac{1}{28}\right)=\frac{5}{3}\cdot\frac{3}{14}=\frac{5}{14}\)