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प्रश्न
Find the sum of the following series up to n terms:
.6 +.66 +. 666 +…
योग
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उत्तर
.6 + .66 + .666 + …..
Let Sn = 0.6 + 0.66 + 0.666 +... to n terms
= 6[0.1 + 0.11 + 0.111 + ........ to n terms]
= `6/9 [0.9 + 0.99 + 0.999 + ....... "to n terms"]`
= `6/9[(1 - 1/10) + (1 - 1/10^2) + (1 - 1/10^3) + ...... "to n terms"]`
= `2/3 [(1 + 1 + ....... "to n terms") - 1/10 (1 + 1/10 + 1/10^2 + ....... "to n terms")]`
= `2/3 ["n" - 1/10((1 - (1/10)^"n")/(1 - 1/10))]`
= `2/3"n" - 2/30 xx 10/9 (1 - 10^(-"n"))`
= `2/3"n" - 2/27 (1 - 10^-"n")`
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