Question

1. $y_1 + y_2 + y_3 + y_4 + y_5 + y_6 + y_7 + y_8$

(a) $sum_{i=8}^1 y$
(b) $sum_{i=1}^8 y_i$
(c) $sum_1^i y_8$
(d) $sum_i^8 y_1$

Explanation:

Step1: Analyze the summation notation

The sum \(Y_1 + Y_2+Y_3 + Y_4+Y_5 + Y_6+Y_7 + Y_8\) is a sum of terms where the index \(i\) starts at \(1\) and ends at \(8\).
The general form of a summation is \(\sum_{i = m}^{n}a_i=a_m + a_{m + 1}+\cdots+a_n\).
Here \(a_i=Y_i\), \(m = 1\) and \(n=8\).

Step2: Check each option

• Option A: \(\sum_{i = 8}^{1}Y\) is not in the correct form (the index should be in the sub - script and super - script of the summation symbol for the terms, and the lower limit \(8\) and upper limit \(1\) with the wrong variable \(Y\) (should be \(Y_i\))).
• Option B: \(\sum_{i=1}^{8}Y_i=Y_1 + Y_2+Y_3 + Y_4+Y_5 + Y_6+Y_7 + Y_8\)
• Option C: \(\sum_{1}^{i}Y_8\) has the wrong index variable (the terms do not depend on \(i\) in the correct way as the original sum)
• Option D: \(\sum_{i}^{8}Y_1\) has the wrong index variable (the terms do not depend on \(i\) in the correct way as the original sum)

Answer:

B. \(\sum_{i = 1}^{8}Y_i\)