Question

Consider the sum $\underset{i=p}{\overset{q}{\sum b_i}}$

(a) Write out this sum in expanded form (i.e., without sigma notation).

(b) What is the index of the sum? What is the starting value? What is the ending value? Which part of the notation describes the form of each of the terms in the sum?

(c) Do p and q have to be integers? Can they be negative? What about $b_i$? What else can you say about p and q?

Short answer

Part(a) $b_p+b_{p+1}+...b_{q-1}+b_q$

Part(b) Index of the sum is i,starting value and ending value are p and q.

Part(c) Yes, and cannot be negative.

Step-by-step solution

Part(a) Step 1. Given Information

The given expression is$\underset{i=p}{\overset{q}{\sum b_i}}$

Part(a) Step 2. Explanation

In the expanded form, the notation sigma is not used.

The expanded form is$b_p+b_{p+1}+...b_{q-1}+b_q$

Part(b) Step 1. Explanation

Since, $i=p$and the sum to be found is for $b_i$ So the index is i.

The summation starts and ends with $i=pandi=q$respectively so the starting and ending value is $pandq$respectively.

The term $b_i$describes the from of each of the terms in the sum.

Part(c) Step 1. Explanation

Yes, p and q needs to be integers and cannot be negative. They must be positive integers, $b_i$needs to be any real number.

The addition condition of p and q is$p\le q$