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Limit of (p(x) - p(a))/(x - a) for a sum of powers

This type of question, asked 2 times: 4 May 2023 S2, 23 Apr 2025 S1. All 2 questions below, oldest first.

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  1. Question 1

    4 May 2023 S2

    130
    If f(x)=x+x2+x3+…+xn−nx−1f(x)=\frac{x+x^2+x^3+\ldots+x^n-n}{x-1}, for x≠1x\neq1 is continuous at x=1x=1, then f(1)=f(1)=

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  2. Question 2

    23 Apr 2025 S1

    108
    lim⁡x→2x+3x2+5x3+7x4−166x−2=\lim_{x\rightarrow 2} \frac{x+ 3x^{2}+ 5x^{3}+ 7x^{4}- 166}{x- 2}=

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