If sum of the first 21 terms of the series ${\log _{{9^{1/2}}}}x + {\log _{{9^{1/3}}}}x + {\log _{{9^{1/4}}}}x + .......$, where x > 0 is 504, then x is equal to
Solution
$s = 2{\log _9}x + 3{\log _9}x + ....... + 22{\log _9}x$<br><br>$s = {\log _9}x(2 + 3 + ..... + 22)$<br><br>$s = {\log _9}x\left\{ {{{21} \over 2}(2 + 22)} \right\}$<br><br>Given, $252{\log _9}x = 504$<br><br>$\Rightarrow {\log _9}x = 2 \Rightarrow x = 81$
About this question
Subject: Mathematics · Chapter: Sequences and Series · Topic: Arithmetic Progression
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