WBJEE · Maths · Definite Integration
The sum of the series
\(\frac{1}{1 \times 2}^{25} C_{0}+\frac{1}{2 \times 3}{ }^{25} C_{1}+\frac{1}{3 \times 4}{ }^{25} C_{2}+\ldots \\
+\frac{1}{26 \times 27}{ }^{25} C_{25} \text { is }\)
- A \(\frac{2^{27}-1}{26 \times 27}\)
- B \(\frac{2^{27}-28}{26 \times 27}\)
- C \(\frac{1}{2}\left(\frac{2^{26}+1}{26 \times 27}\right)\)
- D \(\left(\frac{2^{26}-1}{52}\right)\)
Answer & Solution
Correct Answer
(B) \(\frac{2^{27}-28}{26 \times 27}\)
Step-by-step Solution
Detailed explanation
Given series is, \(\frac{1}{1 \times 2} \stackrel{25}{C_{0}}+\frac{1}{2 \times 3}{ }^{25} C_{1}+\frac{1}{3 \times 4}{ }^{25} C_{2}\) \(+\ldots+\frac{1}{26 \times 27}^{25} \mathrm{C}_{25}\)…
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