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Question

Find (55+11)2n+1 - (5511)2n+1


A

2[2n+1C1(55)2n(11)1 - 2n+1C2(55)2n1(11)2..............]

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B

2[2n+1C1(55)2n(11)1 + 2n+1C2(55)2n1(11)2..............]

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C

2[(55)2n+1 + 2n+1C2(55)2n1(11)2..............]

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D

2[(55)2n+1 - 2n+1C2(55)2n1(11)2..............]

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Solution

The correct option is B

2[2n+1C1(55)2n(11)1 + 2n+1C2(55)2n1(11)2..............]


(55+11)2n+1 = (55)2n+1 + 2n+1C1(55)2n(11)1 + 2n+1C2(55)2n1(11)2.......... ..............(1)

(5511)2n+1 = (55)2n+1 - 2n+1C1(55)2n(11)1 - 2n+1C2(55)2n1(11)2.......... ..............(2)

(1) - (2) gives

(55+11)2n+1 - (5511)2n+1 = 2[2n+1C1(55)2n(11)1 + 2n+1C2(55)2n1(11)2..............]


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