For all $n\in N$, $\frac{n^5}{5}+\frac{n^3}{3}+\frac{7n}{15}$ is a$$

Important Questions on Mathematical Induction

MEDIUM

Mathematics

IMPORTANT

Mathematics Crash Course BITSAT>Chapter 15 - Mathematical Induction>Exercise 1>Q 34

For each natural number $n,$ $4^n-1$ is divisible by

HARD

Mathematics

IMPORTANT

Mathematics Crash Course BITSAT>Chapter 15 - Mathematical Induction>Exercise 1>Q 35

For all natural numbers $n$, $n^3-7n+3$ is divisible by 

MEDIUM

Mathematics

IMPORTANT

Mathematics Crash Course BITSAT>Chapter 15 - Mathematical Induction>Exercise 1>Q 36

The statement : $n^3+{\left(n+1\right)}^3+{\left(n+2\right)}^3$ is an integer multiple of 

MEDIUM

Mathematics

IMPORTANT

Mathematics Crash Course BITSAT>Chapter 15 - Mathematical Induction>Exercise 1>Q 37

If $P\left(n\right)$ is the statement that $\text{'}{7}^{2n}-1$ is divisible by $48\text{'}$ and if $P\left(r\right)$ is true, then $P\left(r+1\right)$ is divisible by

EASY

Mathematics

IMPORTANT

Mathematics Crash Course BITSAT>Chapter 15 - Mathematical Induction>Exercise 1>Q 38

If $P\left(n\right):2^n<n!$, then the smallest positive integer for which $P\left(n\right)$ is true if

EASY

Mathematics

IMPORTANT

Mathematics Crash Course BITSAT>Chapter 15 - Mathematical Induction>Exercise 1>Q 39

If $P\left(n\right):{}^{\text{'}\text{'}}2^{2n}-1$ is divisible by $k$ for all $n\in N^{\text{'}\text{'}}$ is true, then the value of $k$ is

EASY

Mathematics

IMPORTANT

Mathematics Crash Course BITSAT>Chapter 15 - Mathematical Induction>Exercise 1>Q 40

For all$n\in N$ and $n\ge 3, 2^{4n}-2^n\left(7n+1\right)$ is not divisible by