Define in [tex]\mathbb{R}[/tex]:

[tex]\[ (x+1)(x+3) = (x+2)^2 + 1 \][/tex]

Calculate:

[tex]\[ R = 1 + 2 + 3 + \cdots + 10 \][/tex]

A) 25

B) 30

C) 45



Answer :

Answer:

To solve the problem, we first need to calculate the value of \( R \), which is defined as:

\[ R = 1 + 2 + 3 + \cdots + 10 \]

This is the sum of the first 10 positive integers. We can use the formula for the sum of the first \( n \) positive integers:

\[ S_n = \frac{n(n + 1)}{2} \]

where \( n \) is the number of terms. Here, \( n = 10 \). Plugging in this value:

\[ S_{10} = \frac{10(10 + 1)}{2} = \frac{10 \times 11}{2} = 55 \]

So, the sum \( R \) is 55. However, since none of the given choices (A, B, C) match this result, it seems there might have been a misunderstanding or an error in the options provided. The correct result is:

\[ R = 55 \]