CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

Let $$P\left ( n \right ):n^{2}+n$$ is an odd integer
$$P\left ( k \right )\Rightarrow P\left ( k+1 \right )$$ is true
Then $$P\left ( n \right )$$ is true for all


A
n>2
loader
B
n>1
loader
C
n
loader
D
none of these
loader

Solution

The correct option is A none of these
Given that $$P\left( n \right) :{ n }^{ 2 }+n$$ is an odd integer.

$$P\left( k \right) \Rightarrow P\left( k+1 \right) $$ is true.

For $$P\left( n \right) $$ to be true for all $$n$$, it should be true for $$n=1$$

$$P\left( 1 \right) ={ 1 }^{ 2 }+1=2$$ This is not an odd integer, So not true for $$n=1$$

Check for $$n=2$$, $$P\left( 2 \right) ={ 2 }^{ 2 }+2=6$$ This is again not odd, 

so not true for $$n=2$$

For $$n=3$$, $$P\left( 3 \right) ={ 3 }^{ 2 }+3=9$$, odd so true

For $$n=4$$, $$P\left( 4 \right) ={ 4 }^{ 2 }+4=20$$ not odd, so not true.

 So we see from options, it not true for any given option.

Mathematics

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
People also searched for
View More



footer-image