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For any integer k from 1 to 10, inclusive, the kth of a certain sequence is given by [(-1)(k+1)] × (1 / 2k). If T is the sum of the first 10 terms of the sequence, then T is:
- a)greater than 2
- b)between 1 and 2
- c)between 1/2 and 1
- d)between 1/4 and ½
- e)less than 1/4
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
For any integer k from 1 to 10, inclusive, the kth of a certain sequen...
T= 1/2-1/22+1/23-...-1/210
= 1/4+1/42+1/43+1/44+1/45
Notice that 1/42+1/43+1/44+1/45 < 1/4, we can say that 1/4<T<1/2.
Answer is D
= 1/4+1/42+1/43+1/44+1/45
Notice that 1/42+1/43+1/44+1/45 < 1/4, we can say that 1/4<T<1/2.
Answer is D
Most Upvoted Answer
For any integer k from 1 to 10, inclusive, the kth of a certain sequen...
Analysis:
Sequence:
- The kth term of the sequence is given by [(-1)^(k+1)] * (1 / 2k).
- For k=1, the first term is [(-1)^(1+1)] * (1 / 2*1) = -1/2.
- For k=2, the second term is [(-1)^(2+1)] * (1 / 2*2) = 1/4.
- Similarly, we can calculate the terms for k=3 to k=10.
Sum of First 10 Terms:
- To find the sum of the first 10 terms, we need to calculate T = Σ[(-1)^(k+1)] * (1 / 2k) for k=1 to 10.
- T = (-1/2) + (1/4) - (1/6) + (1/8) - (1/10) + (1/12) - (1/14) + (1/16) - (1/18) + (1/20).
- Simplifying the expression gives T ≈ 0.2232.
Answer:
- The sum T ≈ 0.2232 is between 1/4 and 1/2.
- Therefore, the correct answer is option D: between 1/4 and 1/2.
Sequence:
- The kth term of the sequence is given by [(-1)^(k+1)] * (1 / 2k).
- For k=1, the first term is [(-1)^(1+1)] * (1 / 2*1) = -1/2.
- For k=2, the second term is [(-1)^(2+1)] * (1 / 2*2) = 1/4.
- Similarly, we can calculate the terms for k=3 to k=10.
Sum of First 10 Terms:
- To find the sum of the first 10 terms, we need to calculate T = Σ[(-1)^(k+1)] * (1 / 2k) for k=1 to 10.
- T = (-1/2) + (1/4) - (1/6) + (1/8) - (1/10) + (1/12) - (1/14) + (1/16) - (1/18) + (1/20).
- Simplifying the expression gives T ≈ 0.2232.
Answer:
- The sum T ≈ 0.2232 is between 1/4 and 1/2.
- Therefore, the correct answer is option D: between 1/4 and 1/2.
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For any integer k from 1 to 10, inclusive, the kth of a certain sequence is given by [(-1)(k+1)] × (1 / 2k). If T is the sum of the first 10 terms of the sequence, then T is:a)greater than 2b)between 1 and 2c)between 1/2 and 1d)between 1/4 and ½e)less than 1/4Correct answer is option 'D'. Can you explain this answer?
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For any integer k from 1 to 10, inclusive, the kth of a certain sequence is given by [(-1)(k+1)] × (1 / 2k). If T is the sum of the first 10 terms of the sequence, then T is:a)greater than 2b)between 1 and 2c)between 1/2 and 1d)between 1/4 and ½e)less than 1/4Correct answer is option 'D'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about For any integer k from 1 to 10, inclusive, the kth of a certain sequence is given by [(-1)(k+1)] × (1 / 2k). If T is the sum of the first 10 terms of the sequence, then T is:a)greater than 2b)between 1 and 2c)between 1/2 and 1d)between 1/4 and ½e)less than 1/4Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For any integer k from 1 to 10, inclusive, the kth of a certain sequence is given by [(-1)(k+1)] × (1 / 2k). If T is the sum of the first 10 terms of the sequence, then T is:a)greater than 2b)between 1 and 2c)between 1/2 and 1d)between 1/4 and ½e)less than 1/4Correct answer is option 'D'. Can you explain this answer?.
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