The common term of the sequence \( \frac{1}{n} \) is \( \frac{1}{10} \). To find the value of \( s_{10} \) (the sum of the first 10 terms), you can use the formula for the sum of the first \( n \) terms of a sequence, which is \( s_n = \frac{n}{2} \cdot (a_1 + a_n) \). In this case, \( a_1 \) is the first term (\( \frac{1}{1} \)) and \( a_{10} \) is the 10th term (\( \frac{1}{10} \)).
So, \( s_{10} = \frac{10}{2} \cdot \left(\frac{1}{1} + \frac{1}{10}\right) \). Calculate this expression to find the value of \( s_{10} \).
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Answer:
The common term of the sequence \( \frac{1}{n} \) is \( \frac{1}{10} \). To find the value of \( s_{10} \) (the sum of the first 10 terms), you can use the formula for the sum of the first \( n \) terms of a sequence, which is \( s_n = \frac{n}{2} \cdot (a_1 + a_n) \). In this case, \( a_1 \) is the first term (\( \frac{1}{1} \)) and \( a_{10} \) is the 10th term (\( \frac{1}{10} \)).
So, \( s_{10} = \frac{10}{2} \cdot \left(\frac{1}{1} + \frac{1}{10}\right) \). Calculate this expression to find the value of \( s_{10} \).