Question

find the sum of the series -' 7+77+777+.......... upto infinity'

Answer 1

Answer:

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Step-by-step explanation:

7, 77, 777, 7777 ….to n terms.

Sn=7+77+777+7777+……+to n terms

introducing 9

= (7/9) [9+99+999+……+ to n terms]

= (7/9) [(10-1) + (100-1) + (1000-1) +……...+ to n term]

= (7/9) [10+100+1000+……... n terms – (1+1+1+1+…… n terms)

= (7/9) [10+100+1000+………n terms –n]

Here a=10, r=10

= (7/9) [10(10n-1)/ (9) - n]

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