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Name the number sequence that we will get when we start to Eda powers of 2 starting with one and then add one to each of these numbers?
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Name the number sequence that we will get when we start to Eda powers ...
Understanding the Sequence
The sequence you will generate by taking powers of 2 starting from one and then adding one to each of these numbers is known as the "2-adic numbers" or more commonly, the "one more than powers of 2" sequence.
Generating the Sequence
To create this sequence, follow these steps:
- Start with the first power of 2: 2^0 = 1
- Add 1 to this value: 1 + 1 = 2
- Proceed to the next power of 2: 2^1 = 2
- Add 1: 2 + 1 = 3
- Continue this process for higher powers of 2.
Resulting Numbers
The resulting sequence based on this pattern will be as follows:
- 2^0 + 1 = 2
- 2^1 + 1 = 3
- 2^2 + 1 = 5
- 2^3 + 1 = 9
- 2^4 + 1 = 17
- 2^5 + 1 = 33
- 2^6 + 1 = 65
Thus, the final sequence generated will be:
- 2, 3, 5, 9, 17, 33, 65, ...
Properties of the Sequence
- Each term in the sequence is one more than a power of 2.
- The sequence grows exponentially as the powers of 2 increase.
- This sequence is useful in various mathematical contexts, including number theory and computer science.
By following these steps, you can easily generate the sequence by adding one to each power of 2, revealing interesting properties related to exponential growth.
The sequence you will generate by taking powers of 2 starting from one and then adding one to each of these numbers is known as the "2-adic numbers" or more commonly, the "one more than powers of 2" sequence.
Generating the Sequence
To create this sequence, follow these steps:
- Start with the first power of 2: 2^0 = 1
- Add 1 to this value: 1 + 1 = 2
- Proceed to the next power of 2: 2^1 = 2
- Add 1: 2 + 1 = 3
- Continue this process for higher powers of 2.
Resulting Numbers
The resulting sequence based on this pattern will be as follows:
- 2^0 + 1 = 2
- 2^1 + 1 = 3
- 2^2 + 1 = 5
- 2^3 + 1 = 9
- 2^4 + 1 = 17
- 2^5 + 1 = 33
- 2^6 + 1 = 65
Thus, the final sequence generated will be:
- 2, 3, 5, 9, 17, 33, 65, ...
Properties of the Sequence
- Each term in the sequence is one more than a power of 2.
- The sequence grows exponentially as the powers of 2 increase.
- This sequence is useful in various mathematical contexts, including number theory and computer science.
By following these steps, you can easily generate the sequence by adding one to each power of 2, revealing interesting properties related to exponential growth.
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Name the number sequence that we will get when we start to Eda powers of 2 starting with one and then add one to each of these numbers?
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Name the number sequence that we will get when we start to Eda powers of 2 starting with one and then add one to each of these numbers? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Name the number sequence that we will get when we start to Eda powers of 2 starting with one and then add one to each of these numbers? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Name the number sequence that we will get when we start to Eda powers of 2 starting with one and then add one to each of these numbers?.
Name the number sequence that we will get when we start to Eda powers of 2 starting with one and then add one to each of these numbers? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Name the number sequence that we will get when we start to Eda powers of 2 starting with one and then add one to each of these numbers? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Name the number sequence that we will get when we start to Eda powers of 2 starting with one and then add one to each of these numbers?.
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