What is the remainder when 7 + 77 + 777 + 7777 + …. (till 100 terms) is divided by 8?
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7+77+777+.....100terms
=7(1+11+111+......100terms)
=7/9(9+99+999....100terms)
actually here I multiplied 1 11 111 s with 9 and divided 7 out there by 9 so as to keep the value same. I hope u understand .
=7/9(10+100+1000+...100times-1-1-1....100times)
now I added 1 to each term in the backer and kept all negative 1s aside to keep it simple.
now the 10 100 1000 makes a GP.
formula for summation of a finite GP is
1st term(ratio between terms^last term -1)/(ratio between terms -1)
so, putting values in formula,we get,
(7/9)(10^100 -1)/(10-1)
if we divide this by 8, we get,
(7/648)(10^100-1)
u think of after steps
and try to find answer
=7(1+11+111+......100terms)
=7/9(9+99+999....100terms)
actually here I multiplied 1 11 111 s with 9 and divided 7 out there by 9 so as to keep the value same. I hope u understand .
=7/9(10+100+1000+...100times-1-1-1....100times)
now I added 1 to each term in the backer and kept all negative 1s aside to keep it simple.
now the 10 100 1000 makes a GP.
formula for summation of a finite GP is
1st term(ratio between terms^last term -1)/(ratio between terms -1)
so, putting values in formula,we get,
(7/9)(10^100 -1)/(10-1)
if we divide this by 8, we get,
(7/648)(10^100-1)
u think of after steps
and try to find answer
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