Question

7+77+777........nth term


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Answer 1

I hope it will help you

Answer 2

Answer:

7/9 [ 10/9 ( 10ⁿ - 1 ) ] - n

Step-by-step explanation:

7 + 77 + 777 + .... n terms

Taking common term we get,

⇒ 7 ( 1 + 11 + 111 + ... n terms )

Multiplying and dividing by 9 we get,

⇒ 7 / 9 × 9 ( 1 + 11 + 111 + ... n terms )

⇒ 7 / 9 ( 9 + 99 + 999 + ... n terms )

9 can be written as 10 - 1.

99 can be written as 100 - 1

999 can be written as 1000 - 1

Similarly all can be written in the form 10ⁿ⁻¹ - 1

So we can write it as:

⇒ 7/9 ( 10 - 1 + 100 - 1 + 1000 - 1 + .... 10ⁿ⁻¹ - 1 )

⇒ 7/9 ( 10 + 100 + 1000 + ... 10ⁿ⁻¹  ) - 1 ( 1 + 1 + 1 ... n terms )

⇒ 7/9 [ 10/10-1 ( 10ⁿ - 1 ) ] - n

⇒ 7/9 [ 10/9 ( 10ⁿ - 1 ) ] - n

This is the required answer.

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