JEE Mains · Maths · STD 11 - 8. sequence and series
If \(S=\frac{7}{5}+\frac{9}{5^{2}}+\frac{13}{5^{3}}+\frac{19}{5^{4}}+\ldots .\), then \(160 \mathrm{~S}\) is equal to....... .
- A \(200\)
- B \(305\)
- C \(400\)
- D \(505\)
Answer & Solution
Correct Answer
(B) \(305\)
Step-by-step Solution
Detailed explanation
\(\mathrm{S} =\frac{7}{5}+\frac{9}{5^{2}}+\frac{13}{5^{3}}+\frac{19}{5^{4}}+\ldots\) \(\frac{1}{5} \mathrm{~S} =\frac{7}{5^{2}}+\frac{9}{5^{3}}+\frac{13}{5^{4}}+\ldots\) On subtracting \(\frac{4}{5} S=\frac{7}{5}+\frac{2}{5^{2}}+\frac{4}{5^{3}}+\frac{6}{5^{4}}+\ldots\)…
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