Question:
Consider an+1 = 1/1+1/an for n = 1,2,.......2008,2009. where a1 = 1. Find the value of a1a2 + a2a3 + a3a4+ .......+ a2008a2009.
Consider an+1 = 1/1+1/an for n = 1,2,.......2008,2009. where a1 = 1. Find the value of a1a2 + a2a3 + a3a4+ .......+ a2008a2009.
Updated On: Aug 9, 2024
- 2009/1000
- 2009/2008
- 2008/2009
- 6000/2009
- 2008/6000
Hide Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Given that,
a1 = 1
a2 = 1/1+1/1 = 1/2
a3 = 1/1+1/1/2 = 1/1+2 = 1/3
Similarly, a4 = 1/4, a5 = 1/5, .......... a2008 = 1/2008, a2009 = 1/2009
a1a2 + a2a3 + a3a4 + .......... + a2008a2009
= 1x1/2 + 1/2x1/3 + 1/3x1/4 ....... + 1/2008x1/2009
= 2-1/1x2 + 3-2/2x3 + 4-3/3x4 + ......2008-2007/2007x2008 + 2009-2008/2008x2009
= 1-1/2+1/2-1/3+1/3-1/4 .........1/2007-1/2008+1/2008-1/2009
= 1-1/2009
= 2008/2009
Hence, option C is the correct answer.
Was this answer helpful?
1
0
Top Questions on Number Systems
- There are 10 stations on a railway line.The number of different journey tickets that are require by the authorities, is
- If abc > 0, such that a,b,c are integers then which of the following must be true?
- If the digit in the unit's place of a two-digit number is halved and the digit in ten's place is doubled, the number thus obtained is equal to the number obtained by interchanging the digits. Which of the following is definitely true?
- Prove that $\sqrt{3}$ is an irrational number.
- CBSE Class X - 2024
- Mathematics
- Number Systems
- Consider a 4-digit number of the form abbb, i.e., the first digit is a (a > 0) and the last three digits are all b.
Which of the following conditions is both NECESSARY and SUFFICIENT to ensure that the 4- digit number is divisible by a?
View More Questions
Questions Asked in XAT exam
- Arya, a graduate from a reputable institute, got a job in an IT company but became bored after a year. Her best friend S, who worked at the same company, joined a top-tier B-school for an MBA, which tempted Arya to pursue the same path. Her friend assured her that an MBA would boost her career prospects and salary. Arya started preparing for an MBA while continuing her job, but the challenge of balancing preparation with work made her consider leaving the job.
- XAT - 2025
- Analytical Decision Making
- There’s a community 30 km outside of the main city. Mr. S started a grocery business in the community after winning the bid by offering way above the rent initially drafted by the community council. The community council, led by Mr. D, agreed to the offer with a performance review every three years. Mr. S also agreed to provide an additional 15% of his grocery sales to the council, banking on the prospect of selling in higher volumes. After setting up his business, Mr. S noticed that SUV owners in the community usually bought goods in bulk from the city once a week and used his store primarily for daily necessities and occasional big purchases like mixer grinders.
- XAT - 2025
- Analytical Decision Making
- Four reviewers (R1, R2, R3, R4) are in charge of reviewing products from companies A, B, C, and D. Each reviewer provides a rating between 1 and 5 for the products. Due to a technical glitch, the original ratings were deleted, and only the averages calculated for each product (A, B, C, D) and each reviewer (R1, R2, R3, R4) were saved. The data available is as follows:Tasks:
A B C D Average 3 4 4 ? 4 3 ? 5 ? 4 ? 3 3 ? 4 ? ? ? ? 4.25 4 4 4 4.25
1. What are the missing values in the table?
2. How were the missing values calculated?
3.Verify the correctness of the given averages for both rows and columns. - In an 8-week course, the teacher conducts a test every week, and the scores are in the range of 1–4. There are only two students enrolled in the course, \(R\) and \(S\). The following conditions are given:
- \(R\) and \(S\) scored the same on the first test.
- From the second test onwards, \(R\) consistently scored the same (a non-zero score).
- The total of the first three test scores of \(R\) equals the total of the first two test scores of \(S\).
- From the fifth test onwards, \(S\) scored the same as \(R\).
- The scores of \(S\) from the first two tests and all the remaining tests follow a geometric progression.
- XAT - 2025
- Algebra
- An iron beam made with rare materials has its market price dependent on the square of its length. The beam broke into two pieces in the ratio of 4 : 9. If it is sold as two separate pieces, what would be the percentage profit or loss compared to its original value?
- XAT - 2025
- Profit and Loss
View More Questions