Question

C = 1/1x6 + 1/6 x 11 + 1/11 x 16 + ....... + 1/2011 x 2016

Answer 1

\(C=\frac{1}{1.6}+\frac{1}{6.11}+\frac{1}{11.16}+...+\frac{1}{2011.2016}\)

\(5C=\frac{5}{1.6}+\frac{5}{6.11}+\frac{5}{11.16}+...+\frac{5}{2011.2016}\)

\(5C=1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+...+\frac{1}{2011}-\frac{1}{2016}\)

\(5C=1-\frac{1}{2016}\)

\(5C=\frac{2015}{2016}\)

\(C=\frac{2015}{2016}:5\)

\(C=\frac{403}{2016}\)

Answer 2

Đặt A =  \(\frac{1}{1\times6}+\frac{1}{6\times11}+\frac{1}{11\times16}+...+\frac{1}{2011\times2016}\)

\(A\times5=\frac{5}{1\times6}+\frac{5}{6\times11}+\frac{5}{11\times16}+...+\frac{5}{2011\times2016}\)

\(A\times5=\frac{1}{1}-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+...+\frac{1}{2011}-\frac{1}{2016}\)

\(A\times5=\frac{1}{1}-\frac{1}{2016}\)

\(A=\frac{2015}{2016}\times\frac{1}{5}\)

\(A=\frac{2015}{10080}=\frac{403}{2016}\)