Question

Consider the sum$\sum _{k=2}^5\frac{k}{1-k}$. Identify the terms$a_2,a_3,a_4,a_5$

Short answer

The terms are$a_2=-2,a_3=-\frac{3}{2},a_4=-\frac{4}{3},a_5=-\frac{5}{4}$

Step-by-step solution

Step 1. Given Information 

The given expression is$\sum _{k=2}^5\frac{k}{1-k}$

Step 2. Calculation

From the given expression, the general form to find the term is $\frac{k}{1-k}$.

Substitute $k=2,3,4,5$in the general form to find the required terms.

$$\begin{gathered} a_2=\frac{2}{1-2}=-2 \\ {a}_3=\frac{3}{1-3}=-\frac{3}{2} \\ {a}_4=\frac{4}{1-4}=-\frac{4}{3} \\ {a}_5=\frac{5}{1-5}=-\frac{5}{4} \end{gathered}$$