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8. Sequences and Series
medium
$6 + 66 + 666 + …..(n $ પદ સુધી $) = ….$
A
$\frac{{{{10}^{n - 1}} - 9n + 10}}{{81}}$
B
$\frac{{2({{10}^{n + 1}} - 9n - 10)}}{{27}}$
C
$\frac{{2({{10}^n} - 9n - 10)}}{{27}}$
D
આમાંથી એક પણ નહિ.
Solution
$ = \frac{6}{9}(9 + 99 + 999 + …n\,$ પદ સુધી $)$
$ = \frac{2}{3}[10 + {10^2} + {10^3} + ….. + (n$ પદ સુધી $)$ $ {\text{ – n]}}$
$ = \frac{2}{3}\left[ {\frac{{10({{10}^n} – 1)}}{{10 – 1}} – n} \right]\,\,\, = \frac{2}{{27}}[{10^{n + 1}} – 10 – 9n]\,\,\, = \frac{{2({{10}^{n + 1}} – 9n – 10)}}{{27}}$
Standard 11
Mathematics
