Find the sum of the sequence 7, 77, 777...

Find the sum of the sequence 7, 77, 777, 7777, . . . to n terms.

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AI Generated Solution

To find the sum of the sequence 7, 77, 777, 7777, ..., up to n terms, we can follow these steps: ### Step 1: Identify the pattern in the sequence The sequence can be expressed as: - 1st term: 7 - 2nd term: 77 = 7 × 11 - 3rd term: 777 = 7 × 111 - 4th term: 7777 = 7 × 1111 ...

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The sum of the sequence 5 + 55 + 555 + ….. Upto n terms is

`(5)/(9)[(10(10^(n) -1)+n)/(9)]`

`(5)/(9)[(10(10^(n) -1))/(9)-n]`

`(5)/(9)[(10(10^(n+1) -1))/(9)-n]`

`(5)/(9)[(10(10^(n-1) -1))/(9)-n]`

Find the sum of the series 3 + 7 + 13 + 21 + 31 + … to n terms . Find the sun when n=20

`(n(n^(2) + 2n + 3))/(3), 3110`

`(n(n^(2) + 3n + 5))/(3), 3110`

`(n(n^(2) + 3n + 5))/(3) , 3120`

`(n(n^(2) + 2n +2))/(3), 3120`

The sum of the sequence upto 5, 55, 555, …. upto n infinite terms is

`(5)/(9) [(10(10^(n)-1)+n)/(9)]`

`(5)/(9) [(10(10^(n)-1))/(9)-n]`

`(5)/(9) [(10(10^(npm1)-1))/(9)-n]`

`(5)/(9) [(10(10^(n-1)-1))/(9)-n]`