Question

Tính 

S=2/1.4+2/4.7+2/7.10+....+2/97.100

Answer 1

A=2/1.4+2/4.7+2/7.10+...+2/97.100

=2/3(3/1.4+3/4.7+3/7.10+...+3/97.100)

=2/3(1-1/4+1/4-1/7+1/7-1/10+...+1/97-1/100)

=2/3(1-1/100)=33/50

Answer 2

\(S=\frac{2}{1.4}+\frac{2}{4.7}+\frac{2}{7.10}+......+\frac{2}{97.100}\)

\(\Rightarrow S=\frac{2}{3}\left(\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+....+\frac{3}{97.100}\right)\\ \Rightarrow S=\frac{2}{3}\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+....+\frac{1}{97}-\frac{1}{100}\right)\\ \Rightarrow S=\frac{2}{3}\left(1-\frac{1}{100}\right)\\ \Rightarrow S=\frac{33}{50}\)

Answer 3

A=2/1.4+2/4.7+2/7.10+...+2/97.100

=2/3 (3/1.4+3/4.7+3/7.10+...+3/97.100)

=2/3 (1-1/4+1/4-1/7+1/7-1/10+...+1/97-1/100)

=2/3 (1-1/100)=33/50

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