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Question

P(n):1+3+5+...+2n1=n2

The statement P(n) is 



Correct Answer
A

is true for all natural numbers

Your Answer
B

is not true for n>1

Your Answer
C

is true for n>2

Your Answer
D

none of these


Solution

The correct option is A

is true for all natural numbers


P(n):1+3+5+...+2n1=n2P(1):1=121=1 true
Assume P(k) is true
1+3+5+...+2k1=k2Now, P(k+1):1+3+5+...+2n1+2k+1=k2+2k+1=(k+1)2

P(k+1) is also true.
Hence, P(n) is true for all natural numbers

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