Find the sum of the following series :

9 + 99 + 999 + … to n terms.

Taking 9 in common we get


9(1 + 11 + 111 + ....n)


Now Multiply and Divide by 9 we get,


)


)




Now first term is in GP.


10, 100, 1000…to n terms


Common Ratio = r =


Sum of GP for n terms = …(1)


a = 10, r = 10, n = n


Substituting the above values in (1) we get




For the second term the summation is n.



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