Show by the Principle of Mathematical induction that the sum \( S_{n} \) of the \( n \) terms of... VIDEO
Show by the Principle of Mathematical induction that the sum \( S_{n} \) of the \( n \) terms of the series \( 1^{2}+2 \times 2^{2}+3^{2}+2 \times 4^{2} \) \( +5^{2}+2 \times 6^{2}+7^{2}+\ldots \) is given byhttps://bit.ly/YTAI_PWAP https://www.pw.live
Other Videos By PW Solutions 2023-06-19 Some physical quantities are given in Column-I and some possible SI Units in which these quantit... 2023-06-19 Match Column-I with Column-II and select the correct answer using the codes given below the list... 2023-06-19 Statement-I: A screw gauge having a smaller value of pitch has greater accuracy.
Statement-II: T... 2023-06-19 The difference between an + ve integer and its cube is divisible by-
(a) 4
(b) 6
(c) 9
(d) None ... 2023-06-19 Statement-I: Specific gravity of a fluid is a dimensionless quantity.
Statement-II: It is the ra... 2023-06-19 Statement-I: Unit chosen for measuring physical quantities should not be accessible.
Statement-I... 2023-06-19 Statement-I: For each natural number \( n,(n+1)^{7}-n^{7}-1 \) is divisible by 7 .
Statement-II:... 2023-06-19 Column-I gives three physical quantities. Select the appropriate units for the choices given in ... 2023-06-19 Statement-I: When percentage errors in the measurement of mass and velocity are \( 1 \% \) and \... 2023-06-19 Match the physical quantities given in Column-I with dimensions expressed in terms of mass (M), ... 2023-06-19 Show by the Principle of Mathematical induction that the sum \( S_{n} \) of the \( n \) terms of... 2023-06-19 There are four Vernier scales, whose specifications are given in column-I and the least count is... 2023-06-19 Let \( S(k)=1+3+5+\ldots \ldots+(2 k-1)=3+k^{2} \), then which of the following is true?
(a) \( ... 2023-06-19 Prove that
\[
\frac{1}{2} \tan \left(\frac{x}{2}\right)+\frac{1}{4} \tan \left(\frac{x}{4}\right... 2023-06-19 Using significant figures, match the following.
\begin{tabular}{|l|l|c|l|}
\hline \multicolumn{2... 2023-06-19 A sequence \( x_{0}, x_{1}, x_{2}, x_{3}, \ldots \) is defined by letting \( x_{0}=5 \) and \( x... 2023-06-19 Mark the correction alternative in the following: A student was asked to prove a statement \( P(... 2023-06-19 Given \( a_{1}=\frac{1}{2}\left(a_{0}+\frac{A}{a_{0}}\right), a_{2}=\frac{1}{2}\left(a_{1}+\frac... 2023-06-19 Given \( a_{1}=\frac{1}{2}\left(a_{0}+\frac{A}{a_{0}}\right), a_{2}=\frac{1}{2}\left(a_{1}+\frac... 2023-06-19 Prove that \( \sin x+\sin 3 x+\ldots+\sin (2 n-1) x=\frac{\sin ^{2} n x}{\sin x} \) for all \( n... 2023-06-19 Prove that \( \cos \alpha+\cos (\alpha+\beta)+\cos (\alpha+2 \beta)+\ldots+\cos \)
\[
(\alpha+(n...
0