Solution:
It is given that 5n−1<3n+1, where n is a natural number. By inspection, we can say that the inequality holds when n=1,2,34, and 5 .
Now, we need to find the least integer value of m that satisfies 3n+1<2n+m
For, n=1, the least integer value of m is 2 .
For, n=2, the least integer value of m is 3
For, n=3, the least integer value of m is 4 .
For, n=4, the least integer value of m is 4 .
For, n=5, the least integer value of m is 5 .
Hence, the least integer value of m such that for all the values of n, the equation holds is 5 .
© examsnet.com