Grace M.

asked • 07/23/18

Sum the series 9+99+999+9999+...to n terms

Sum the series 9+99+999+9999+...to n terms ( with the working well shown and its 5 marks)

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Anita A. answered • 07/23/18

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a1 = 101-1 = 9; a2 == 102-1 = 99; a3 103-1 = 999; a4 = 104 -1 = 9999; a5 = 105 -1 = 99999; an = 10n-1
 
s1 = 9 = 9
s2 = 9+99 = 108
s3 = 9+99+999 = 1107
s4 = 9+99+999+9999 = 11106
s5 = 9+99+999+9999+99999 = 11105
 
(i=1) ∑ (i=n) (10n - 1)
 
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