Question:
Find the greatest integral power of 2 in 41! + 42! + 43! + ……………+ 50!
Find the greatest integral power of 2 in 41! + 42! + 43! + ……………+ 50!
Updated On: Sep 10, 2024
- 32
- 38
- 44
- 28
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The Correct Option is B
Solution and Explanation
Greatest integral power of 2 in 41! is : 20 + 10 + 5 + 2 + 1 = 38
Now, 41! + 42! + 43! + ……………+ 50!
41! × (1 + 42 + 43 × 42 + 44 × 43 × 42 + ………………)
41! × (1 + even)
41! × (odd)
Since, the bracket is odd, so we don’t have any extra power of 2 other than 38.
So, the correct option is (B) : 38.
Now, 41! + 42! + 43! + ……………+ 50!
41! × (1 + 42 + 43 × 42 + 44 × 43 × 42 + ………………)
41! × (1 + even)
41! × (odd)
Since, the bracket is odd, so we don’t have any extra power of 2 other than 38.
So, the correct option is (B) : 38.
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