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find the sum of 7,77,777,7777,up to nth term
Asked by kbhavani936 | 19 Feb, 2024, 02:46: PM

S = 7 + 77 + 777 + 7777 + ............................ to n terms

S = 7( 1 + 11 + 111 + 1111 + ......................... to n terms  )

S = 7 [ 1 + (1+10) + (1+10+100 ) + (1+10+100+1000) + ......................to n terms  ]

In above expression , each term is geometric progression with first term = 1 and common ratio 10 .

where sr = 1 + 10 + 100 +  ............10r = ( 10r - 1 ) / (10-1) = (1/9) ( 10r - 1 )

Answered by Thiyagarajan K | 19 Feb, 2024, 06:10: PM

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