Question: Can all kinds of summation be transformed into a Riemann Sum so that it can be transformed into a definite integral?

Consider this limit: $$\begin{align} L=\lim\limits_{n\to\infty}\sum_{i=1}^n\dfrac{m\left[a+i\dfrac{b-a}{n}\right]+c}{m\left[a+(i-1)\dfrac{b-a}{n}\right]+c}, \end{align}$$

where $a, b, c, m$ are non-zero and $b>a$. I searched other answers and some are using squeeze theorem, which I don't know how to apply to this problem. Can someone show me step-by-step procedure on how to transform this sum into definite integral?


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.