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Answer :
Sure! Let's determine which of the given expressions is closest to [tex]\( e \)[/tex].
The value of [tex]\( e \)[/tex] is approximately 2.718.
We need to evaluate the following expressions:
1. [tex]\( \left(1+\frac{1}{25}\right)^{25} \)[/tex]
2. [tex]\( \left(1+\frac{1}{24}\right)^{24} \)[/tex]
3. [tex]\( \left(1+\frac{1}{25}\right)^{26} \)[/tex]
4. [tex]\( \left(1+\frac{1}{23}\right)^{23} \)[/tex]
Let's compute the values of these expressions:
1. [tex]\( \left(1+\frac{1}{25}\right)^{25} \approx 2.665836 \)[/tex]
2. [tex]\( \left(1+\frac{1}{24}\right)^{24} \approx 2.663731 \)[/tex]
3. [tex]\( \left(1+\frac{1}{25}\right)^{26} \approx 2.772470 \)[/tex]
4. [tex]\( \left(1+\frac{1}{23}\right)^{23} \approx 2.661450 \)[/tex]
Next, we calculate how close each expression is to the value of [tex]\( e \)[/tex] by finding the absolute differences between each expression's value and [tex]\( e \)[/tex]:
1. [tex]\( |2.665836 - 2.718| \approx 0.052 \)[/tex]
2. [tex]\( |2.663731 - 2.718| \approx 0.054 \)[/tex]
3. [tex]\( |2.772470 - 2.718| \approx 0.054 \)[/tex]
4. [tex]\( |2.661450 - 2.718| \approx 0.057 \)[/tex]
Among these differences, the smallest difference is [tex]\( 0.052 \)[/tex], which corresponds to the expression [tex]\( \left(1+\frac{1}{25}\right)^{25} \)[/tex].
Therefore, the value of the expression closest to [tex]\( e \)[/tex] is:
[tex]\[ \left(1+\frac{1}{25}\right)^{25} \][/tex]
So, the correct answer is:
A. [tex]\( \left(1+\frac{1}{25}\right)^{25} \)[/tex]
The value of [tex]\( e \)[/tex] is approximately 2.718.
We need to evaluate the following expressions:
1. [tex]\( \left(1+\frac{1}{25}\right)^{25} \)[/tex]
2. [tex]\( \left(1+\frac{1}{24}\right)^{24} \)[/tex]
3. [tex]\( \left(1+\frac{1}{25}\right)^{26} \)[/tex]
4. [tex]\( \left(1+\frac{1}{23}\right)^{23} \)[/tex]
Let's compute the values of these expressions:
1. [tex]\( \left(1+\frac{1}{25}\right)^{25} \approx 2.665836 \)[/tex]
2. [tex]\( \left(1+\frac{1}{24}\right)^{24} \approx 2.663731 \)[/tex]
3. [tex]\( \left(1+\frac{1}{25}\right)^{26} \approx 2.772470 \)[/tex]
4. [tex]\( \left(1+\frac{1}{23}\right)^{23} \approx 2.661450 \)[/tex]
Next, we calculate how close each expression is to the value of [tex]\( e \)[/tex] by finding the absolute differences between each expression's value and [tex]\( e \)[/tex]:
1. [tex]\( |2.665836 - 2.718| \approx 0.052 \)[/tex]
2. [tex]\( |2.663731 - 2.718| \approx 0.054 \)[/tex]
3. [tex]\( |2.772470 - 2.718| \approx 0.054 \)[/tex]
4. [tex]\( |2.661450 - 2.718| \approx 0.057 \)[/tex]
Among these differences, the smallest difference is [tex]\( 0.052 \)[/tex], which corresponds to the expression [tex]\( \left(1+\frac{1}{25}\right)^{25} \)[/tex].
Therefore, the value of the expression closest to [tex]\( e \)[/tex] is:
[tex]\[ \left(1+\frac{1}{25}\right)^{25} \][/tex]
So, the correct answer is:
A. [tex]\( \left(1+\frac{1}{25}\right)^{25} \)[/tex]
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