Question

TÍNH:

1/2.6 + 1/6.10 + 1/10.14 + ..... + 1/102.106

Answer 1

Đặt A = 1/2.6 + 1/6.10 + 1/10.14 + ..... + 1/102.106

=> 4A = 4/2.6 + 4/6.10 + 4/10.14 + ..... + 4/102.106

=> 4A = 1/2 - 1/6 + 1/6 - 1/10 + 1/10 - 1/14 + ... + 1/102 - 1/106

=> 4A = 1/2 - 1/106

=> 4A = 26/53

=> A = 13/106

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Answer 2

\(\frac{1}{2.6}+\frac{1}{6.10}+...+\frac{1}{102.106}\)

\(=\frac{1}{4}.\left(\frac{4}{2.6}+\frac{4}{6.10}+...+\frac{4}{102.106}\right)\)

\(=\frac{1}{4}.\left(\frac{1}{2}-\frac{1}{6}+\frac{1}{6}-\frac{1}{10}+...+\frac{1}{102}-\frac{1}{106}\right)\)

\(=\frac{1}{4}.\left(\frac{1}{2}-\frac{1}{106}\right)\)

\(=\frac{1}{4}.\frac{26}{53}\)

\(=\frac{13}{106}\)

Answer 3

Đặt \(B=\frac{1}{2.6}+\frac{1}{6.10}+\frac{1}{10.14}+...+\frac{1}{102.106}\)

\(\Leftrightarrow4B=\frac{4}{2.6}+\frac{4}{6.10}+\frac{4}{10.14}+...+\frac{4}{102.106}\)

\(\Leftrightarrow4B=\frac{1}{2}-\frac{1}{6}+\frac{1}{6}-\frac{1}{10}+\frac{1}{10}-\frac{1}{14}+...+\frac{1}{102}-\frac{1}{106}\)

\(\Leftrightarrow4B=\frac{1}{2}-\frac{1}{106}=\frac{26}{53}\)

\(\Leftrightarrow B=\frac{26}{53}:4=\frac{13}{106}\)

Vậy ...................

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Answer 4

#)Giải :

Đặt \(S=\frac{1}{2.6}+\frac{1}{6.10}+\frac{1}{10.14}+...+\frac{1}{102.106}\)

\(\Rightarrow4S=\frac{4}{2.6}+\frac{4}{6.10}+\frac{4}{10.14}+...+\frac{4}{102.106}\)

\(\Rightarrow4S=\frac{1}{2}-\frac{1}{6}+\frac{1}{6}-\frac{1}{10}+\frac{1}{10}-\frac{1}{14}+...+\frac{1}{102}-\frac{1}{106}\)

\(\Rightarrow4S=\frac{1}{2}-\frac{1}{106}\)

\(\Rightarrow4S=\frac{26}{53}\)

\(\Leftrightarrow S=\frac{13}{106}\)

Answer 5

Đặt M= \(\frac{1}{2\cdot6}+\frac{1}{6\cdot10}+\frac{1}{10\cdot14}+....+\frac{1}{102\cdot106}\)

\(\Rightarrow4M=\frac{4}{2\cdot6}+\frac{4}{6\cdot10}+\frac{4}{10\cdot14}+...+\frac{4}{102\cdot106}\)

\(\Rightarrow4M=\frac{1}{2}-\frac{1}{6}+\frac{1}{6}-\frac{1}{10}+\frac{1}{10}-\frac{1}{14}+...+\frac{1}{102}-\frac{1}{106}\)

\(\Rightarrow4M=\frac{1}{2}-\frac{1}{106}=\frac{26}{53}\)

\(\Rightarrow M=\frac{26}{53}\cdot\frac{1}{4}=\frac{13}{106}\)

Answer 6

= 1/2 -1/6+1/6-1/10+1/10-1/14+ ...+1/102-1/106

= 1/2-1/106

=52/106  =26/53

Answer 7

\(\frac{1}{2.6}+\frac{1}{6.10}+\frac{1}{10.14}+...+\frac{1}{102.106}\)

\(=\frac{1}{4}.\left(\frac{1}{2}-\frac{1}{6}+\frac{1}{6}-\frac{1}{10}+\frac{1}{10}-\frac{1}{14}+...+\frac{1}{102}-\frac{1}{106}\right)\)

\(=\frac{1}{4}.\left(\frac{1}{2}-\frac{1}{106}\right)\)

\(=\frac{1}{4}.\frac{26}{53}=\frac{13}{106}\)