Find the sum of 5 55 555 n terms
Asked by admin @ in Math viewed by 351 People
5+55+555+5555+.......nth term sum=?
Answered by admin @
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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