MCQ
શ્રેણી $6 + 66 + 666 + ..........$ નો $n$ પદ સુધી સરવાળો કરો.
- A$({10^{n - 1}} - 9n + 10)/81$
- ✓$2({10^{n + 1}} - 9n - 10)/27$
- C$2({10^n} - 9n - 10)/27$
- Dએકપણ નહિ.
$ = \frac{6}{9}(9 + 99 + 999 + .....$ upto $n$ terms)
$ = \frac{2}{3}(10 + {10^2} + {10^3} + .......... + $ upto $n$ terms $ - n$)
$ = \frac{2}{3}\left( {\frac{{10({{10}^n} - 1)}}{{10 - 1}} - n} \right) = \frac{1}{{27}}\,[20({10^n} - 1) - 18n]$
$ = \frac{{2({{10}^{n + 1}} - 9n - 10)}}{{27}}$.
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