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21(i)  Find the sum of the following series up to n terms:  

             5 + 55+ 555 + ....

Answers (1)

best_answer

5 + 55+ 555 + .... is not a GP.

It can be changed in GP by writing terms as 

S_n=5 + 55+ 555 + .... to n terms

S_n=\frac{5}{9}[9+99+999+9999+................]

S_n=\frac{5}{9}[(10-1)+(10^2-1)+(10^3-1)+(10^4-1)+................]

S_n=\frac{5}{9}[(10+10^2+10^3+........)-(1+1+1.....................)]

S_n=\frac{5}{9}[\frac{10(10^n-1)}{10-1}-(n)]

S_n=\frac{5}{9}[\frac{10(10^n-1)}{9}-(n)]

S_n=\frac{50}{81}[(10^n-1)]-\frac{5n}{9}

Thus, the sum is 

      S_n=\frac{50}{81}[(10^n-1)]-\frac{5n}{9}

Posted by

seema garhwal

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