Question

A= 1/2 +1/6 + 1/12 + 1/20 + 1/30 + 1/42 + 1/56 A= 1/2x1

Answer 1

\(A=\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{42}+\dfrac{1}{56}\)

\(A=\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+\dfrac{1}{5.6}+\dfrac{1}{6.7}+\dfrac{1}{7.8}\)

\(A=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}\)

\(A=1-(\dfrac{1}{2}-\dfrac{1}{2})+(\dfrac{1}{3}-\dfrac{1}{3})+(\dfrac{1}{4}-\dfrac{1}{4})+(\dfrac{1}{5}-\dfrac{1}{5})+(\dfrac{1}{6}-\dfrac{1}{6})+(\dfrac{1}{7}-\dfrac{1}{7})-\dfrac{1}{8}\)

\(A=1-\dfrac{1}{8}\)

\(A=\dfrac{8}{8}-\dfrac{1}{8}\)

\(A=\dfrac{7}{8}\)

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\(A=\dfrac{1}{2}.1=\dfrac{1}{2}\)

Answer 2

a,A=\(\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{42}\)

A=\(\dfrac{1}{1\times2}+\dfrac{1}{2\times3}+...+\dfrac{1}{6\times7}\)

A=\(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{6}-\dfrac{1}{7}\)

A=\(1-\dfrac{1}{7}\)

A=\(\dfrac{6}{7}\)

b,A=\(\dfrac{1}{2}\times1\)

A=\(\dfrac{1}{2}\)