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but it does not work. Can someone say what went wrong, i.e, Why doesn"t the integral give sầu $S$ as I mentioned first?

I realized now that this is more a sequence rather than a series. A sequence is a phối of numbers which are resulted from a general term where as a series is a phối of functional elements; the derivative of elements of a sequence is zero & its integration is pointless. So using the integration of general term of a sequence khổng lồ find its sum is just not needed.

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algebra-precalculus summation arithmetic-progressions geometric-progressions
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edited Jan 13 "17 at 0:34
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Timothy Cho
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asked Sep 29 "16 at 18:45
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siroussirous
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$egingroup$
$$eginalign*S &= sum_i=1^n (10^i-1)/9 \<6pt>&= frac19 left(sum_i=1^n 10^i - sum_i=1^n 1 ight) \<6pt>&= frac19 left(frac109(10^n -1) - n ight) \<6pt>&= frac1081 (10^n -1) - fracn9endalign*$$


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edited Sep 30 "16 at 0:12
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Au101
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answered Sep 29 "16 at 18:52
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ZubzubZubzub
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