Embibe Experts Solutions for Exercise 2: Assignment

Mathematical induction is a tool or technique which is used to prove a proposition about all

For each $n\in N,3^{2n}-1$ is divisible by

The statement $n!>2^{n-1},n\in N$ is true for

The proposition among the following that is not true for all $n\in N$, is

 If $7+77+777+\dots$ upto $n^{\text{th }}$ term $=\frac{7}{81}\left[a·{10}^{n+1}-bn-c\right]$ is true $\forall n\in N$, then

The proposition that is not true for $n>1(n\in N)$ is

For all $n(>1)\in N$, by using mathematical induction or otherwise $1+\frac{1}{2}+\frac{1}{3}+\dots +\frac{1}{n}$ in its lowest form is

The sum of the squares of three consecutive odd numbers increased by $1$ is divisible by (use mathematical induction)