Question

Tinh tong:

S1=1/2+ 1/6+ 1/12+ 1/20 + 1/30 +  1/42 + 1/56+ 1/72 +1/90.

Giup mk vs nhe ,mk se tick. 

Answer 1

\(S1=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}\)

\(S1=\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+\frac{1}{6\cdot7}+\frac{1}{7\cdot8}+\frac{1}{8\cdot9}+\frac{1}{9\cdot10}\)

\(S1=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}\)

\(S1=1-\frac{1}{10}\)

\(S1=\frac{9}{10}\)

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Answer 2

S=\(\frac{1}{1.2}+\frac{1}{2.3}+...............+\frac{1}{9.10}\)

=\(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...............+\frac{1}{9}-\frac{1}{10}\)

=\(1-\frac{1}{10}\)

=\(\frac{9}{10}\)