Question

B) 4 Σ(+2) (r + 2) r=1
​

Answer 1

The expression you've provided is a sigma notation for the sum of a sequence. In this case, the expression is:

4Σ(+2)(r + 2) evaluated for r starting from 1.

This means we start with r=1 and continue up to some value (let's say n) and add up the values of (+2)(r + 2) for each value of r from 1 to n.

Let's calculate it step by step:

When r=1, the value of (+2)(r + 2) = (+2)(1 + 2) = 3*2 = 6

When r=2, the value of (+2)(r + 2) = (+2)(2 + 2) = 4*2 = 8

When r=3, the value of (+2)(r + 2) = (+2)(3 + 2) = 5*2 = 10

Adding them up: 6 + 8 + 10 = 24

So, 4Σ(+2)(r + 2) r=1 is equal to 24.

Answer 2

The expression \(4 \sum_{r=1}^{+2} (r + 2)\) represents a summation where the variable \(r\) takes values from 1 to 2. Let's calculate it:

\[4 \sum_{r=1}^{2} (r + 2) = 4[(1 + 2) + (2 + 2)]\]

\[= 4 \times (3 + 4) = 4 \times 7 = 28\]

So, \(4 \sum_{r=1}^{+2} (r + 2) = 28\).