Q. 21 B3.9( 26 Votes )

Find the sum of the following series up to n terms:

6 + . 66 + . 666 + …

Answer :

The given sum is not in GP but we can write it as follows: -


Sum = .6 + .66 + .666 + …to n terms


= 6(0.1) + 6(0.11) + 6(0.111) + …to n terms


taking 6 common


= 6[0.1 + 0.11 + 0.111 + …to n terms]


divide & multiply by 9


= (6/9)[9(0.1 + 0.11 + 0.111 + …to n terms)]


= (6/9)[0.9 + 0.99 + 0.999 + …to n terms]






Since is in GP with


first term(a) = 1/10


common ratio(r) = 10 - 2/10 - 1 = 10 - 1 = 1/10


We know that


Sum of n terms = (As r<1)


putting value of a & r






Hence, Sum


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