The sum 1 + 2 . 3 + 3 . 32 + ......... + 10 . 39 is equal to :
Solution
<p>Let $S = 1\,.\,{3^0} + 2\,.\,{3^1} + 3\,.\,{3^2} + \,\,......\,\, + \,\,10\,.\,{3^9}$</p>
<p>$3S = 1\,.\,{3^1} + 2\,.\,{3^2} + \,\,..........\,\, + \,\,10\,.\,{3^{10}}$</p>
<p>___________________________________________________________</p>
<p>$$ - 2S = (1\,.\,{3^0} + 1\,.\,{3^1} + 1\,.\,{3^2} + \,\,........\,\, + \,\,1\,.\,{3^9}) - 10\,.\,{3^{10}}$$</p>
<p>$$ \Rightarrow S = {1 \over 2}\left[ {10\,.\,{3^{10}} - {{{3^{10}} - 1} \over { - 3 - 1}}} \right]$$</p>
<p>$\Rightarrow S = {{19\,.\,{3^{10}} + 1} \over 4}$</p>
About this question
Subject: Mathematics · Chapter: Sequences and Series · Topic: Arithmetic Progression
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