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If 6 3 12 + 10 3 11 + 20 3 10 + 40 3 9 + … . . + 10240 3 = 2 n · m , where m is odd, then m . n is equal to _____ .

Correct answer

0

Step-by-step solution

Given, 6 3 12 + 10 3 11 + 20 3 10 + 40 3 9 + … . . + 10240 3 = 2 n · m On rearranging we get, ⇒ 1 3 12 + 5 2 0 3 12 + 2 1 3 11 + 2 2 3 10 + … … + 2 11 3 = 2 n · m ⇒ 1 3 12 + 5 1 3 12 6 2 - 1 6 - 1 = 2 n · m ⇒ 1 3 12 + 5 5 1 3 12 · 2 12 · 3 12 - 1 3 12 = 2 n · m ⇒ 1 3 12 + 2 12 - 1 3 12 = 2 n · m ⇒ 2 n · m = 2 12 On comparing both side we get, ⇒   m = 1 and n = 12 So, m · n = 12

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