Question

Tính

1/1.3.5 + 1/3.5.7 + 1/5.7.9 + ... + 1/99.101.103

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Answer 1

1/1.3.5 + 1/3.5.7 + 1/5.7.9 +.....+ 1/99.101.103

= 1/4. [4/1.3.5 + 4/3.5.7 + 4/ 5.7.9 +....+ 4/99.101.103]

=1/4. [1/1.3 - 1/3.5 + 1/3.5 - 1/5.7 +....+ 1/99.101 - 1/101.103]

= 1/4. [1/1.3 - 1/101.103]

=1/4. 10406/31209

= 5230/62418

Answer 2

\(A=\frac{1}{1\cdot3\cdot5}+\frac{1}{3\cdot5\cdot7}+....+\frac{1}{99\cdot101\cdot103}\)

\(2A=\frac{1}{1\cdot3}-\frac{1}{3\cdot5}+\frac{1}{3\cdot5}-\frac{1}{5-7}+....+\frac{1}{99\cdot101}-\frac{1}{101\cdot103}\)

\(2A=\frac{1}{1\cdot3}-\frac{1}{101\cdot103}\)

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