A sequence \( x_{0}, x_{1}, x_{2}, x_{3}, \ldots \) is defined by letting \( x_{0}=5 \) and \( x... VIDEO
A sequence \( x_{0}, x_{1}, x_{2}, x_{3}, \ldots \) is defined by letting \( x_{0}=5 \) and \( x_{k}=4+x_{k-1} \) for all natural numbers \( k \). Show that \( x_{n}=5+4 n \) for all \( n \in N \) using mathematical induction.
📲PW App Link - https://bit.ly/YTAI_PWAP
🌐PW Website - https://www.pw.live
Other Videos By PW Solutions 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: For every natural number \( n \geq 2 \)
\( \frac{1}{\sqrt{1}}+\frac{1}{\sqrt{2}}+\l... 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 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 Column-I gives three physical quantities. Select the appropriate units for the choices given in ... 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 Prove that \( \cos \alpha+\cos (\alpha+\beta)+\cos (\alpha+2 \beta)+\ldots+\cos \)
\[
(\alpha+(n... 2023-06-19 Prove that \( \frac{(2 n) !}{2^{2 n}(n !)^{2}} \leq \frac{1}{\sqrt{3 n+1}} \) for all \( n \in N \) 2023-06-19 There are four Vernier scales, whose specifications are given in column-I and the least count is... 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 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 Mark the correction alternative in the following: A student was asked to prove a statement \( P(... 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 the following by the principle of mathematical induction:
\[
a+a r+a r^{2}+\ldots+a r^{n-1... 2023-06-19 For all \( n \in N, \sum n \)
(a) \( \frac{(2 n+1)^{2}}{8} \)
(b) \( \frac{(2 \mathrm{n}+1)^{2}}... 2023-06-19 \( 1+2+3+\ldots \ldots+n\frac{(n+2)^{2}}{8}, n \in N \), is true for
(a) \( n \geq 1 \)
(b) \( n... 2023-06-19 The inequality \( n !2^{n-1} \) is true
(a) For all \( n1 \)
(b) For all \( n2 \)
(c) For all \(... 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 If \( \mathrm{n} \) is a natural number then \( \left(\frac{\mathrm{n}+1}{2}\right)^{\mathrm{n}}...