JEE Mains · Maths · STD 11 - 8. sequence and series
If \((20)^{19}+2(21)(20)^{18}+3(21)^2(20)^{17}+\ldots \ldots\). \(+20(21)^{19}= k (20)^{19}\), then \(k\) is equal to
- A \(200\)
- B \(300\)
- C \(400\)
- D \(100\)
Answer & Solution
Correct Answer
(C) \(400\)
Step-by-step Solution
Detailed explanation
\(\text { If }(20)^{19}+2(21)(20)^{18}+3(21)^2(20)^{17}+\ldots+20(21)^{19}=\) \(k (20)^{19}\) then \(k\) is \(20^{19}\left(1+2 \cdot\left(\frac{21}{20}\right)+3\left(\frac{21}{20}\right)^2+\ldots+20\left(\frac{21}{20}\right)^{19}\right)=k(20)^{19}\)…
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