TS EAMCET · Maths · Sequences and Series
Let the greatest common divisor of \(m, n\) be 1 . If \(\frac{1}{1 \cdot 7}+\frac{1}{7 \cdot 13}+\frac{1}{13 \cdot 19}+\ldots . .\). upto 20 terms \(=\frac{m}{n}\), then \(5 m+2 n=\)
- A 325
- B 330
- C 342
- D 337
Answer & Solution
Correct Answer
(C) 342
Step-by-step Solution
Detailed explanation
(c) We have, \(\begin{aligned} & \frac{m}{n}=\frac{1}{1 \cdot 7}+\frac{1}{7 \cdot 13}+\frac{1}{13 \cdot 19}+\ldots+\frac{1}{[1+(20-1) 6][7+(20-1) 6]} \\ & =\frac{1}{1 \cdot 7}+\frac{1}{7 \cdot 13}+\frac{1}{13 \cdot 19}+\ldots+\frac{1}{115 \times 121} \end{aligned}\)…
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