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Question

Let N be the set of natural numbers. Suppose f:NN is a function satisfying the following conditions :
(a) f(m+n)=f(m)+f(n)(b) f(2)=2
Then the value of 1720k=1f(k) is

A
35
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B
40
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C
30
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D
20
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Solution

The correct option is C 30
f(m+n)=f(m)+f(n)
Putting m=n=1, we get
f(2)=2f(1)=2f(1)=1
Putting m=2,n=1, we get
f(3)=f(2)+f(1)=3
Putting m=n=2, we get
f(4)=2f(2)=4
Similarly, f(n)=n

Therefore, f(x)=x for all xN
Now, 1720k=1f(k)
=1720k=1k=20×217×2=30

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