Let $P(n): 2+2^2+2^3+\ldots+2^n=2^{n+1}-2, n \in N$. Then,
- A$P(m)$ is true $\Rightarrow P(m+1)$ is true
- B$P(n)$ is true for all $n \in N$
- C$P(n)$ is true for all $n \geq 20$
- D$P(n)$ is true for all $n \leq 10$
Explore More
Similar Questions
Consider the statement: $P(n): n^2 - n + 41$ is prime. Then which one of the following is true?
DifficultJEE MAIN 2019
View SolutionUse the Principle of Mathematical Induction to show that $\frac{n^{5}}{5}+\frac{n^{3}}{3}+\frac{7n}{15}$ is a natural number for all $n \in N$.
Medium
View SolutionIf $n$ is a positive integer,then $n^{3}+2n$ is divisible by
If $n \in N$,then the statement $8n + 16 \leq 2^n$ is true for:
Prove the following by using the principle of mathematical induction for all $n \in N$:
$1 \cdot 3 + 2 \cdot 3^{2} + 3 \cdot 3^{3} + \ldots + n \cdot 3^{n} = \frac{(2n - 1) 3^{n+1} + 3}{4}$
$1 \cdot 3 + 2 \cdot 3^{2} + 3 \cdot 3^{3} + \ldots + n \cdot 3^{n} = \frac{(2n - 1) 3^{n+1} + 3}{4}$
Difficult
View SolutionVedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo