Determine the first 3 terms of the sequence given by the general formula
$a_{n}=\frac{1}{n!+1}$

• A. $\left\lbrace\frac12,\frac13,\frac17\right\rbrace$
• B. $\left\lbrace\frac12,\frac13,\frac14\right\rbrace$
• C. $\left\lbrace1,2,7\right\rbrace$
• D. $\left\lbrace1,\frac12,\frac16\right\rbrace$

Answer: (A)

Verified step by step guidance

1. Step 1: Understand the general formula for the sequence, which is a_n = 1 / (n! + 1). Here, n! represents the factorial of n, and the sequence is defined for positive integers n.
2. Step 2: To find the first term (a_1), substitute n = 1 into the formula: a_1 = 1 / (1! + 1). Simplify the factorial and the expression to determine the value of a_1.
3. Step 3: To find the second term (a_2), substitute n = 2 into the formula: a_2 = 1 / (2! + 1). Simplify the factorial and the expression to determine the value of a_2.
4. Step 4: To find the third term (a_3), substitute n = 3 into the formula: a_3 = 1 / (3! + 1). Simplify the factorial and the expression to determine the value of a_3.
5. Step 5: Combine the results from steps 2, 3, and 4 to list the first three terms of the sequence.