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

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

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`f(x)=(x^(100))/(100)+(x^(99))/(99)+...+(x^2)/2+x+1`

`f'(x)=x^(99)+x^(98)+...+x+1+0`

`f'(1)=1^(99)+1^(98)+...+1+1+0=100`

`f'(0)=0^(99)+0^(98)+...+0+1+0=1`

`100f'(0)=100`

Hence, `100f'(0)=f'(1)`
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