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  • Find the sum to n terms of the sequence, 8, 88, 888, 8888… .

18.   Find the sum to n terms of the sequence, 8, 88, 888, 8888… .

Answers (1)

best_answer

 8, 88, 888, 8888… is not a GP.

It can be changed in GP by writing terms as 

S_n=8+88+888+8888+............. to n terms

S_n=\frac{8}{9}[9+99+999+9999+................]

S_n=\frac{8}{9}[(10-1)+(10^2-1)+(10^3-1)+(10^4-1)+................]

S_n=\frac{8}{9}[(10+10^2+10^3+........)-(1+1+1.....................)]

S_n=\frac{8}{9}[\frac{10(10^n-1)}{10-1}-(n)]

S_n=\frac{8}{9}[\frac{10(10^n-1)}{9}-(n)]

S_n=\frac{80}{81}(10^n-1)-\frac{8n}{9}

Posted by

seema garhwal

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