According to ques: \[P\left( n \right)\text{ }=\text{ }{{n}^{2}}~\text{ }n\text{ }+\text{ }41\] is prime. \[P\left( n \right)\text{ }=\text{ }{{n}^{2}}~\text{ }n\text{ }+\text{ }41\] Or,...
Give an example of a statement P (n) such that it is true for all n ϵ N
Let , \[P\text{ }\left( n \right)\text{ }=\text{ }1\text{ }+\text{ }2\text{ }+\text{ }3\text{ }+\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }+\text{ }n\text{ }=\text{ }n\left( n+1 \right)/2~\]...
If P (n) is the statement “n2 + n” is even”, and if P (r) is true, then P (r + 1) is true
According to ques: \[P\text{ }\left( n \right)\text{ }=\text{ }{{n}^{2}}~+\text{ }n\] is even and P (r) is true, then \[{{r}^{2}}~+\text{ }r\] is even Let \[{{r}^{2}}~+\text{ }r\text{ }=\text{...
If P (n) is the statement “2n ≥ 3n”, and if P (r) is true, prove that P (r + 1) is true.
According to ques: \[P\text{ }\left( n \right)\text{ }=\text{ }{{2}^{n}}~\ge \text{ }3n\] and p(r) is true. Now, \[P\text{ }\left( n \right)\text{ }=\text{ }{{2}^{n}}~\ge \text{ }3n\] Since,...
If P (n) is the statement “n3 + n is divisible by 3”, prove that P (3) is true but P (4) is not true.
According to ques: \[P\text{ }\left( n \right)\text{ }=\text{ }{{n}^{3}}~+\text{ }n\] is divisible by 3 Now, \[P\text{ }\left( n \right)\text{ }=\text{ }{{n}^{3}}~+\text{ }n\] Hence,...
If P (n) is the statement “n (n + 1) is even”, then what is P (3)?
According to ques: \[P\text{ }\left( n \right)\text{ }=\text{ }n\text{ }\left( n\text{ }+\text{ }1 \right)\] is even. Hence, \[P\text{ }\left( 3 \right)\text{ }=\text{ }3\text{ }\left( 3\text{...