JEE Mains · Maths · STD 11 - 8. sequence and series
Let \(\quad S=109+\frac{108}{5}+\frac{107}{5^2}+\ldots \ldots . .+\frac{2}{5^{107}}+\frac{1}{5^{108}}\). Then the value of \(\left(16 S -(25)^{-34}\right)\) is equal to \(............\).
- A \(2174\)
- B \(2175\)
- C \(2173\)
- D \(2172\)
Answer & Solution
Correct Answer
(B) \(2175\)
Step-by-step Solution
Detailed explanation
\(S=109+\frac{108}{5}+\frac{107}{5^2} \ldots .+\frac{1}{5^{108}}\) \(\frac{\frac{S}{5}=\frac{109}{5}+\frac{108}{5^2} \ldots \ldots+\frac{2}{5^{108}}+\frac{1}{5^{109}}}{\frac{4 S }{5}=109-\frac{1}{5}-\frac{1}{5^2} \ldots \ldots-\frac{1}{5^{108}}-\frac{1}{5^{109}}}\)…
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