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" equality "n!>2^(n-1)" is true for "...

" equality "n!>2^(n-1)" is true for "

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Assertion: 1+2 + 3 + ... n = (n(n+1))/2 Reason: In a statement P(n), if P(l) is true and assuming P(k) and if we prove P(k + 1) is also true then P(n) is true for all value n, n is true integer

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) be the statement: 2^(n)>=3n. If P(r) is true,show that P(r+1) is true.Do you conclude that P(n) is true for all n in N