This is a problem from Test of Mathematics, TOMATO problem 6. It is useful for ISI and CMI Entrance Exam.

**Problem : TOMATO Problem 6 **

Let be positive integers such that for all where is constant. If then the value of is

(A)

(B)

(C)

(D)

Solution:

We have

for all

Putting in the above relation we obtain,

This gives,

and

Thus,

Now, since

therefore we have,

which, in turn, gives,

.

Therefore, option (B) is the correct option.

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Sequence Problem | ISI Entrance B.Math 2008 Obj 1 – Video

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