Prove that \( I_{1}, I_{2}, I_{3}, \ldots \) form an AP, if
(i) \( ... VIDEO
Prove that \( I_{1}, I_{2}, I_{3}, \ldots \) form an AP, if
(i) \( I_{n}=\int_{0}^{\pi} \frac{\sin 2 n x}{\sin x} d x \)
(ii) \( I_{n}=\int_{0}^{\pi}\left(\frac{\sin n x}{\sin x}\right)^{2} d x \)
P
W.
š²PW App Link - https://bit.ly/YTAI_PWAP
šPW Website - https://www.pw.live
Other Videos By PW Solutions 2023-03-21 Let \( S_{n}=\sum_{k=1}^{4 n}(-1)^{\frac{k(k+1)}{2}} \cdot k^{2} \)... 2023-03-21 Let \( A_{1}, G_{1}, H_{1} \) denote the arithmetic, geometric and ... 2023-03-21 Statement 1 The sum of the series
\[
\begin{aligned}
1+(1+2+4)+(4+6... 2023-03-21 If \( S_{1}, S_{2}, S_{3} \) denote the sum of \( n \) terms of 3 a... 2023-03-21 Suppose four distinct positive numbers \( a_{1}, a_{2}, a_{3}, a_{4... 2023-03-21 Three friends whose ages form a GP divide a certain sum of money in... 2023-03-21 Find the sum to \( n \) terms, whose \( n \)th term is
\[
\tan [\al... 2023-03-21 If \( \sum_{r=1}^{n} T_{r}=\frac{n}{8}(n+1)(n+2)(n+3) \), find \( \... 2023-03-21 Find the sum to infinite terms of the series
\[
\tan ^{-1}\left(\fr... 2023-03-21 If \( \theta_{1}, \theta_{2}, \theta_{3}, \ldots, \theta_{n} \) are... 2023-03-21 Prove that \( I_{1}, I_{2}, I_{3}, \ldots \) form an AP, if
(i) \( ... 2023-03-21 Evaluate \( S=\sum_{n=0}^{n} \frac{2^{n}}{\left(a^{2^{n}}+1\right)}... 2023-03-21 Show that,
\[
\begin{array}{r}
\left(1+5^{-1}\right)\left(1+5^{-2}\... 2023-03-21 If \( \theta_{1}, \theta_{2}, \theta_{3}, \ldots, \theta_{n} \) are... 2023-03-21 If \( a_{1}, a_{2}, a_{3}, \ldots, a_{n} \) are in AP with \( a_{1}... 2023-03-21 Balls are arranged in rows to form an equilateral triangle. The fir... 2023-03-21 Statement-1 (Assertion) and Statement-2 (Reason) Each of these ques... 2023-03-21 Statement-1 (Assertion) and Statement-2 (Reason) Each of these ques... 2023-03-21 \begin{tabular}{l|l|c|c}
\hline \multicolumn{2}{c|}{ Column I } & \... 2023-03-21 Statement-1 (Assertion) and Statement-2 (Reason) Each of these ques... 2023-03-21 Statement-1 (Assertion) and Statement-2 (Reason) Each of these ques...