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प्रश्न
The sum of first n natural numbers is given by `1/2n^2 + 1/2n`. Find the sum of first 11 natural numbers.
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उत्तर
Given, sum of first n natural numbers = `1/2n^2 + 1/2n`
Sum of first 11 natural numbers = `1/2(11)^2 + 1/2(11)` ...[Put n = 11]
= `1/2 xx 121 + 11/2`
= `121/2 + 11/2`
= `132/2`
= 66
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Use the given algebraic expression to complete the table of number patterns.
| S. No |
Expression |
Terms | |||||||||
| 1st | 2nd | 3rd | 4th | 5th | ... | 10th | ... | 100th | ... | ||
| 1 | 2n - 1 | 1 | 3 | 5 | 7 | 9 | - | 19 | - | - | - |
| 2 | 3n + 2 | 5 | 8 | 11 | 14 | - | - | - | - | - | - |
| 3 | 4n + 1 | 5 | 9 | 13 | 17 | - | - | - | - | - | - |
| 4 | 7n + 20 | 27 | 34 | 41 | 48 | - | - | - | - | - | - |
| 5 | n2 + 1 | 2 | 5 | 10 | 17 | - | - | - | - | 10001 | - |
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