JEE Mains · Maths · STD 11 - 7. binomial theoram
The greatest positive integer \(\mathrm{k},\) for which \(49^k+1\) is a factor of the sum \(49^{125}+49^{124}+\ldots .49^{2}+49+1,\) is
- A \(32\)
- B \(60\)
- C \(63\)
- D \(65\)
Answer & Solution
Correct Answer
(C) \(63\)
Step-by-step Solution
Detailed explanation
\(1+49+49^{2}+\ldots+49^{125}\) \(=\frac{(49)^{126}-1}{49-1}=(49^{63}+1) \frac{\left(49^{63}-1\right)}{(48)}\) So greatest value of \(\mathrm{k}=63\)
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