Question

ết: large frac{1}{3x10}+frac{1}{10x17}+frac{1}{17x24}+...+frac{1}{38x45}=frac{6}{x}(Chỉ được chọn 1 đáp án)A.45B.135C.\large \frac{135}{7}D.\large \frac{14}{45}

Answer 1

\(\dfrac{1}{3\cdot10}+\dfrac{1}{10\cdot17}+...+\dfrac{1}{38\cdot45}=\dfrac{6}{x}\)

=>\(\dfrac{1}{7}\left(\dfrac{7}{3\cdot10}+\dfrac{7}{10\cdot17}+...+\dfrac{7}{38\cdot45}\right)=\dfrac{6}{x}\)

=>\(\dfrac{1}{3}-\dfrac{1}{10}+\dfrac{1}{10}-\dfrac{1}{17}+...+\dfrac{1}{38}-\dfrac{1}{45}=\dfrac{42}{x}\)

=>42/45=42/x

=>x=45

=>Chọn A