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Q.

For n∈N,15n5+13n3+715n is

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a

an integer

b

a natural number

c

a positive fraction

d

None of the above

answer is B.

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Detailed Solution

Let P(n):15n5+13n3+715n∴ P(1)=15(1)5+13(1)3+7151 =15+13+715=3+5+715=1515=1∈NP(2)=15(2)5+13(2)3+7152 =325+83+1415 =96+40+1415=15015=10∈NBy mathematical induction P(n) is a natural number

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