MCQ
$1 + 2.2 + 3.2^2 + 4.2^3 +….+ 100.2^{99 } = ........$
- A$99.2^{100}$
- B$100.2^{100}$
- ✓$1 + 99.2^{100}$
- Dઆપેલ પૈકી એકપણ નહિ.
$⇒2S = 2 + 2.2^2 + 3.2^3 + …..99.2^{99 }+ 100.2^{100}$ લેતાં, $ ……(2)$
સમીકરણ $(2)$ માથી સમીકરણ $(1)$ ને બાદ કરતાં ,
$ - {\text{S}} = \left( {{\text{1}} + {\text{2}} + {{\text{2}}^{\text{2}}} + {{\text{2}}^{\text{3}}} + .... + {{\text{2}}^{{\text{99}}}}} \right) - {\text{100}}\,{\text{.}}\,{{\text{2}}^{{\text{100}}}}$ $\Rightarrow \,\,{\text{S}} = {\text{100}}{\text{.}}{{\text{2}}^{{\text{100}}}} - \frac{{{{\text{2}}^{{\text{100}}}} - {\text{1}}}}{{{\text{2}} - {\text{1}}}}$
$ = 100\,{.2^{100}} - {2^{100}} + 1\,\,\,\,\, = 1 + {99.2^{100}}$
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