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For the proposition P(n), given by , 1+3+5+.........+(2n-1) = n^2 +2 , prove that P(k) is true implies P(k + 1) is true. But, P(n) is not true for all n in N.

Let P(n) denotes the statement n^3+(n+1)^3+(n+2)^3 is a multiple of 9 If P(k) is true, prove that P(k+1) is also true

Given P(n):3^(2n) -1 is divisible by 8. If P(k) is true then prove P(k+1) is true.

Consider the statement P(n):2^(3n) -1 is divisible by 7 If p(k) is true, show that p(k+1) is also true

state true or false k[0]=0,k inR

Consider the statement P(n):9^(n)-1 is a multiple of 8, where n is a natural number i. Is P(1) true? ii. Assuming P(k) is true, show that P(k + 1) is also true.

Consider the following statement P(n):A^n=[[cosntheta,sinntheta],[-sinntheta,cosntheta]] for all ninN If P(k) is true then show that P(k+1) is true

Let P(n):n^(2)+n+1 is an even integer.If P(k) is assumed true rArr P(k+1) is true. Therefore P(n) is true:

Consider the statement P(n)=1+3+3^2+…….+3^(n-1)=frac(3^(n)-1)(2) If P(k) is true, prove that P(k+1) is true.

Consider the statement P(n)=1+3+3^2+….+3^(n-1)=(3^n-1)/2 (b)If P(k) is true,prove that P(k+1) is also true.