JEE Mains · Maths · STD 11 - 8. sequence and series
If \({\left( {10} \right)^9} + 2{\left( {11} \right)^1}{\left( {10} \right)^8} + 3{\left( {11} \right)^2}{\left( {10} \right)^7} + ..\;.\;.\;.\; + 10\left( {{{11}^9}} \right) = \;k{\left( {10} \right)^9}\) ,then \(k \) is equal to
- A \(100\)
- B \(110\)
- C \(\frac{{121}}{{10}}\;\)
- D \(\frac{{441}}{{100}}\)
Answer & Solution
Correct Answer
(A) \(100\)
Step-by-step Solution
Detailed explanation
\(k \cdot 10^{9}=10^{9}+2(11)^{1}(10)^{8}+3(11)^{2}(10)^{7}+\ldots\) \(+10(11)^{9}\) \(k=1+2\left(\frac{11}{10}\right)+3\left(\frac{11}{10}\right)^{2}+\ldots 10\left(\frac{11}{10}\right)^{9}\) ......\((i)\)…
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