TS EAMCET · Maths · Sequences and Series
The period of \(\tan k y+\sin k y\), where \(k=1+4+9+\ldots 20\) terms, is
- A \(\frac{\pi}{1435}\)
- B \(\frac{2 \pi}{1435}\)
- C \(\pi\)
- D \(2 \pi\)
Answer & Solution
Correct Answer
(A) \(\frac{\pi}{1435}\)
Step-by-step Solution
Detailed explanation
\(k=1+4+9+\ldots\) upto 20 terms \[ \begin{aligned} & \therefore k=\sum n^2=\frac{n(n+1)(2 n+1)}{6}, \text { where } n=20 \\ & \therefore k=\frac{20 \times 21 \times 41}{6}=70 \times 41=2870 \end{aligned} \] \(\therefore\) Period of tan \(k y\) is \(\frac{2 \pi}{2870}\) and…
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