Question

E = 3²/8x11 +3²/11x14 + 3²/14x17 + ...+ 3²/197x200

Answer 1

\(E=\frac{3^2}{8.11}+\frac{3^2}{11.14}+......+\frac{3^2}{197.200}\)

\(E=3.\left(\frac{3}{8.11}+\frac{3}{11.14}+......+\frac{3}{197.200}\right)\)

\(E=3.\left(\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+.....+\frac{1}{197}-\frac{1}{200}\right)\)

\(E=3.\left(\frac{1}{8}-\frac{1}{200}\right)\)

\(E=3.\frac{3}{25}\)

\(E=\frac{9}{25}\)

Answer 2

\(\frac{1}{3}E=\frac{3}{8x11}+\frac{3}{11x14}+..+\frac{3}{197x200}\)

\(\frac{1}{3}E=\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}+.+\frac{1}{197}-\frac{1}{200}\)

\(\frac{1}{3}E=\frac{1}{8}-\frac{1}{200}\)

\(\frac{1}{3}E=\frac{3}{25}\)

\(E=\frac{9}{25}\)