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2014-04-06T08:44:14+05:30

This Is a Certified Answer

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First of all take 5 common like this
5(1+11+111+....n)
then multiply and divide by 9
5/9*9(1+11+111+....n)
5/9(9+99+999.....n)
now we can write 9 like this
5/9[(10-1)+(10*10-1)+(10*10*10-1).....n)
now 
5/9(10+10*10+10*10*10....n)-[1+1+1+1....n)
so here  a=10, r=10, r>1
so use this formulae
S=a(r to the power n - 1)/r-1
  = 5/9[10(10 to the power n - 1)/10-1] - n
  = 5/9[10/9(10 to the power n - 1) - n
  = 50/81(10 to the power n -1) - 5/9n this is the answer have fun

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2014-04-06T11:30:50+05:30

This Is a Certified Answer

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Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
5+55+555+........
=5(1+11+111+.......)
=5/9(9+99+999+......)
=5/9[(10-1)+(100-1)+(1000-1)+........]
=5/9[(10+100+1000+......n terms)+(-1-1-1......n terms)]
=5/9[10/9(10^n-1)-n] (since,sum of n terms in gp is a(r^n-1)/r-1 where,(r>1))
=5/9[10/9(10^n-1)-n] is the final answer.......
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