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Find the sum of sequence upto n terms 7+77+777+............n?

Find the sum of sequence upto n terms 7+77+777+............n?

Grade:11

1 Answers

Parth Shrivastava
34 Points
11 years ago

Let Sn = 7 + 77 + 777 + … to n terms

 = 7/9 [ 9 + 99 + 999 +....n terms]

 = 7/9 [ (10-1) + (10² - 1) + (10³ - 1) + ....n terms]

 = 7/9 [ (10 + 10² + 10³ +...n terms) - (1+1+1+...n terms) ]

 = 7/9 [ 10(10n - 1)/10-1 - n]

   = 7/9 [ 10( 10n - 1)/9  - n]

 = 70(10n - 1)/81 - 7n/9
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