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For the function f(x)=((x^(100))/(100)...

For the function
`f(x)=((x^(100))/(100)+(x^(99))/(99)+ .......+(x^(2))/2)+x+1`.
prove that f(1)=100f(0).

Text Solution

AI Generated Solution

To solve the problem, we need to evaluate the function \( f(x) \) at \( x = 1 \) and \( x = 0 \), and then show that \( f(1) = 100f(0) \). ### Step-by-Step Solution: 1. **Define the function**: \[ f(x) = \frac{x^{100}}{100} + \frac{x^{99}}{99} + \frac{x^{98}}{98} + \ldots + \frac{x^2}{2} + x + 1 \] ...
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