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A Function f is defined for all positive...

A Function `f` is defined for all positive integers and satisfies `f(1)=2005 and f(1)+f(2)+.............+f(n)=n^2f(n)` for all `n > 1.` Find the value of `f(2004).`

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The correct Answer is:
`1/1002`
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MOTION-FUNCTION-Exercise - 3
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  2. Find the period (if periodic) of the following function ([.] denotes ...

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  3. Find the conjugate of 1/(3-5i)

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  4. Find the period of f(x)=sinx+tanx/2+sinx/(2^2)+t a n x/(2^3)++sinx/(2^...

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  5. Find the period of the function f(x) = (sin x + sin 3x)/(cos x + co...

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  6. A polynomial function f(x) satisfies the condition f(x)f(1/x)=f(x)+f(1...

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  7. Solve the following problems from (i) to (v) on functional equation. (...

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  8. A Function f is defined for all positive integers and satisfies f(1)=2...

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  9. If a, b are positive real numbers such that a-b=2, then find the sma...

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  10. Let f(x)=x^2+kx;k is a real number. The set of values of k for which t...

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  11. Let P(x) is a six degree polynomial with leading coefficient 1 or in o...

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  12. Computer the inverse of the function : f(x) = (x + sqrt(x^(2) + 1))

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  13. Computer the inverse of the function : f (x) = (1+x)/(1-x)

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  14. Computer the inverse of the function : y = (10^(x) - 1)/(10^(x) + 1...

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  15. If f(x)=(a x^2+b)^3, then find the function g such that f(g(x))=g(f(x)...

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  16. If {{:(2+x",", x ge0),(4-x",", x lt 0):}, a then f (f(x)) is given by ...

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  17. Consider the function f(x) = {{:( x^(2) - 1"," , -1 le x le 1) , ( lnx...

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  18. Consider the function f(x) = {{:( x^(2) - 1"," , -1 le x le 1) , ( lnx...

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  19. Consider the function f(x) = {{:( x^(2) - 1"," , -1 le x le 1) , ( lnx...

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  20. The graph of the function y = f(x) is as follows. Match the funct...

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