Answer :

To Prove:



Let us prove this question by principle of mathematical induction (PMI) for all natural numbers


Let P(n):


For n = 1 P(n) is true since


which is divisible by x + y


Assume P(k) is true for some positive integer k , ie,


=


, where m N …(1)


We will now prove that P(k + 1) is true whenever P( k ) is true


Consider ,




[ Adding and subtracting ]


[ Using 1 ]





, which is factor of ( x + y )


Therefore, P (k + 1) is true whenever P(k) is true


By the principle of mathematical induction, P(n) is true for all natural numbers ie, N


Hence proved


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