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

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Text solutionVerified

Solution:

S = 7 + 77 + 777 + 7777 \dots\dots\dots . n t e r m s

S = 7 (1 + 11 + 111 \dots\dots . n t e r m s)

S = \frac{7}{9} (9 + 99 + 999 \dots\dots . n t e r m s)

S = \frac{7}{9} ((10 - 1) + (100 - 1) + (1000 - 1) \dots\dots . n t e r m s)

S = \frac{7}{9} (10 + 100 + 1000 \dots\dots n t e r m s . - (1 + 1 + 1 + 1 \dots . n t e r m s)

S = \frac{7}{9} (\frac{10 ( ( 10 ) ^{n} - 1 )}{10 - 1} - n)

S = \frac{7}{9} (\frac{10 ( ( 10 ) ^{n} - 1 )}{9} - n)

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Question Text	Find the sum of the sequence 7, 77, 777, 7777, . . . to n terms.
Answer Type	Text solution:1
Upvotes	155