Question

G=\(\frac{1}{1\cdot2}\)+\(\frac{2}{2\cdot4}\)+\(\frac{3}{4\cdot8}\)+\(\frac{4}{7\cdot11}\)+\(\frac{5}{11\cdot16}\)

Answer 1

\(G=\frac{1}{1.2}+\frac{2}{2.4}+\frac{3}{4.7}+\frac{4}{7.11}+\frac{5}{11.16}\)

\(G=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}\)

\(G=1-\frac{1}{16}\)

\(G=\frac{15}{16}\)

Answer 2

\(G=\frac{1}{1.2}+\frac{2}{2.4}+\frac{3}{4.7}+\frac{4}{7.11}+\frac{5}{11.16}\)

\(G=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}\)

\(G=1-\frac{1}{16}\)

\(G=\frac{15}{16}\)

Answer 3

\(G=\frac{1}{1.2}+\frac{2}{2.4}+\frac{3}{4.8}+\frac{4}{7.11}+\frac{5}{11.16}\)

\(G=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}\)

\(G=1-\frac{1}{16}=\frac{15}{16}\)