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Question

7+77+777+...n terms =7nk+70m2(10n1)
Find km.
(Note : k and m are positive integers)

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Solution

S=7+77+777+...+n terms.
97S=9+99+999+...
97S=(101)+(1001)+...+(10n1)
97S=(10+100+1000+...+10n)n
97S=10(10n19)n
S=709(10n19)7n9
S=7081(10n1)7n9
Comparing terms,
k=9 and m=9
km=1

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