find the sum of series 8,88,888___up to nterm
Answer (1)
2nd Mar, 2020
Aman, we can calculate the sum by making the series in form of a geometric progression (GP). The answer to this query is calculated to be 8/81 [10^(n+1)- 9n -10]. The solution of your query is as follows:--
Sum of series is 8+88+888+----+nterms
which can be expressed as;
8[1+11+111+---+n terms]
or, 8/9 [9+99+999+----+n terms]
or, 8/9 [(10-1)+ (10^2-1)+ (10^3-1)+----+n terms]
or, 8/9 [ ( 10^1+ 10^2+ 10^3+----+10^n )-(1*n) ] (the darkened series is a GP now)
or, 8/9 [ {10*(10^n-1)/9} -n ] ( using Sum of a GP formula)
which gives on rearranging, 8/81 [10^(n+1)- 9n -10] as the result.
Hope this helps you.
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