Example 15 - Chapter 9 Class 11 Sequences and Series (Term 1)
Last updated at May 29, 2018 by Teachoo
Examples
Example 1 (i)
Example 1 (ii)
Example 2
Example 3 Important
Example 4
Example 5
Example 6 Important
Example 7
Example 8 Important
Example 9
Example 10 Important
Example 11
Example 12 Important
Example 13
Example 14 Important
Example 15 Important You are here
Example 16
Example 17 Important
Example 18 Important
Example 19 Important Deleted for CBSE Board 2022 Exams
Example 20 Deleted for CBSE Board 2022 Exams
Example 21 Important
Example 22
Example 23
Example 24 Important
Chapter 9 Class 11 Sequences and Series (Term 1)
Serial order wise
- Ex 9.1
- Ex 9.2
- Ex 9.3
- Ex 9.4
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Examples
- Miscellaneous
Transcript
Example 15 Find the sum of the sequence 7, 77, 777, 7777, ... to n terms. 7, 77, 777, 7777, ... n terms Here, 77/7 = 11 & 777/77 = 10.09 Thus, ( )/( ) ( )/( ) i.e. common ratio is not same This is not a GP We need to find sum Sum = 7 + 77 + 777 + 7777 + ...upto n terms = 7(1 + 11 + 111 + . upto n terms) = 7(1 + 11 + 111 + . upto n terms) Multiplying & dividing by 9 = 7/9 [9(1 + 11 + 111 + upto n term) = 7/9 [9 + 99 + 999 + 9999 + upto n terms] = 7/9 [(10 1) + (100 1) + (1000 1) + upto n terms] = 7/9 [(10 + 100 + 1000 + .n terms) 1 1 1 upto n terms] = 7/9 [(10 + 100 + 1000 + .n terms) (1 + 1 + 1 + upto n terms)] = 7/9 [(10 + 100 + 1000 + .n terms) n 1] = 7/9 [(10 + 100 + 1000 + .n terms) n] Now, a = 10, r = 10 For, r > 1 i.e. Sn = (a( ^ 1))/( 1) Putting value of a = 10 & r = 10 Sn = (10( 10 ^ 1))/(10 1) Sn = (10( 10 ^ 1))/9 Now substituting this value in (1) Sum = 7/9 [(10 + 102 + 103 + upto n terms) n] Sum = 7/9 [(10( 10 ^ 1))/9 " n" ] Thus, 7, 77, 777, 7777, ...upto n terms = 7/9 [(10( 10 ^ 1))/9 " n" ]
