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Some Convergent Sequences Involving Exponents: For any real number p > 0, the following sequences converge. Fill in each blank with the appropriate value.

1kp→

Short Answer

Expert verified

The required answer is1kp→0

Step by step solution

01

Step 1. Given information   

The given data is for any real numberp > 0, the sequences converge.

02

Step 2. Explanation     

The sequence 1kis a decreasing sequence as k increases 1kdecreases.

For p>0, for increasing k, the terms of the given sequence decreases.

Thus, the given sequence 1kpdecreases.

Hence, 1kp→0as it is a null sequence.

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