Class 11
MATHS
Arithmetic Progressions

# If a_1,a_2,a_3, ,a_n are an A.P. of non-zero terms, prove that 1/(a_1a_2)+1/(a_2a_3)++1/(a_(n-1)a_n)=

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Updated On: 26-5-2020

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227.2 K+

70.3 K+

Text Solution

Solution :
LHS<br> 1/(a_1a_2)+1/(a_2a_3)+...+1/(a_(n-11)a_n)<br> 1/(a_1(a+1+d))+1/(a_2(a_2+d))+...+1/(a_(n-1)(a_(n-1))+d)<br> 1/d(1/a_1-1/(a_1+d))+1/d(1/(a_2+d))<br> 1/d(1/a_1-1/a_2+1/a_2-1/a_3+...+1/(a_(n-1))-1/a_n)<br> 1/d(1/a_1-1/a_n)<br> 1/d((a_n-a_1)/(a_1a_n))<br> 1/d*((n-1)d)/(a_1a_n)<br> (n-1)/(a_1a_n)<br> RHS.

69046316

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289.9 K+

3:02
8488086

8.1 K+

163.2 K+

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69046238

13.8 K+

134.0 K+

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81765

10.7 K+

214.5 K+

5:34
8486686

5.5 K+

110.2 K+

1:33
8487647

1.8 K+

36.1 K+

3:29
8481

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91.7 K+

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1428263

14.4 K+

288.8 K+

6:43
8493563

1.2 K+

24.3 K+

2:53
8487616

2.3 K+

46.9 K+

3:12
30614

54.1 K+

98.4 K+

3:40
8487648

2.1 K+

41.7 K+

6:04
11432172

2.9 K+

57.6 K+

4:13
11433376

2.5 K+

50.4 K+

4:46
8487630

2.6 K+

51.8 K+

2:48
The text passage contains a mathematical question about proving a formula for the sum of a series in an arithmetic progression. The solution to the question is also provided in the text.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
Class 11
MATHS
Arithmetic Progressions

# If a_1,a_2,a_3, ,a_n are an A.P. of non-zero terms, prove that 1/(a_1a_2)+1/(a_2a_3)++1/(a_(n-1)a_n)=

Step by step solution by experts to help you in doubt clearance & scoring excellent marks in exams.

Updated On: 26-5-2020

Apne doubts clear karein ab Whatsapp par bhi. Try it now.

Watch 1000+ concepts & tricky questions explained!

227.2 K+

70.3 K+

Text Solution

Solution :
LHS<br> 1/(a_1a_2)+1/(a_2a_3)+...+1/(a_(n-11)a_n)<br> 1/(a_1(a+1+d))+1/(a_2(a_2+d))+...+1/(a_(n-1)(a_(n-1))+d)<br> 1/d(1/a_1-1/(a_1+d))+1/d(1/(a_2+d))<br> 1/d(1/a_1-1/a_2+1/a_2-1/a_3+...+1/(a_(n-1))-1/a_n)<br> 1/d(1/a_1-1/a_n)<br> 1/d((a_n-a_1)/(a_1a_n))<br> 1/d*((n-1)d)/(a_1a_n)<br> (n-1)/(a_1a_n)<br> RHS.

69046316

14.4 K+

289.9 K+

3:02
8488086

8.1 K+

163.2 K+

6:13
69046238

13.8 K+

134.0 K+

4:48
81765

10.7 K+

214.5 K+

5:34
8486686

5.5 K+

110.2 K+

1:33
8487647

1.8 K+

36.1 K+

3:29
8481

4.6 K+

91.7 K+

3:31
1428263

14.4 K+

288.8 K+

6:43
8493563

1.2 K+

24.3 K+

2:53
8487616

2.3 K+

46.9 K+

3:12
30614

54.1 K+

98.4 K+

3:40
8487648

2.1 K+

41.7 K+

6:04
11432172

2.9 K+

57.6 K+

4:13
11433376

2.5 K+

50.4 K+

4:46
8487630

2.6 K+

51.8 K+

2:48
user
The text passage contains a mathematical question about proving a formula for the sum of a series in an arithmetic progression. The solution to the question is also provided in the text.

TYPE: SINGLE_QUESTION_WITH_ANSWER