Question 7
Given that $f:\mathbb R\to\mathbb R$ such that
$$f(a^2-b^2)=(a-b)(f(a)+f(b))$$
for all real numbers $a$ and $b$, and that $f(1)=\dfrac1{101}$, find the value of $\displaystyle\sum_{k=1}^{100}f(k)$.
$$f(a^2-b^2)=(a-b)(f(a)+f(b))$$
for all real numbers $a$ and $b$, and that $f(1)=\dfrac1{101}$, find the value of $\displaystyle\sum_{k=1}^{100}f(k)$.