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Question
Find (5√5+11)2n+1 - (5√5−11)2n+1
Find (5√5+11)2n+1 - (5√5−11)2n+1
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Solution
The correct option is B 2[2n+1C1(5√5)2n(11)1 + 2n+1C2(5√5)2n−1(11)2..............]
(5√5+11)2n+1 = (5√5)2n+1 + 2n+1C1(5√5)2n(11)1 + 2n+1C2(5√5)2n−1(11)2.......... ..............(1)
(5√5−11)2n+1 = (5√5)2n+1 - 2n+1C1(5√5)2n(11)1 - 2n+1C2(5√5)2n−1(11)2.......... ..............(2)
(1) - (2) gives
(5√5+11)2n+1 - (5√5−11)2n+1 = 2[2n+1C1(5√5)2n(11)1 + 2n+1C2(5√5)2n−1(11)2..............]
2[2n+1C1(5√5)2n(11)1 + 2n+1C2(5√5)2n−1(11)2..............]
(5√5+11)2n+1 = (5√5)2n+1 + 2n+1C1(5√5)2n(11)1 + 2n+1C2(5√5)2n−1(11)2.......... ..............(1)
(5√5−11)2n+1 = (5√5)2n+1 - 2n+1C1(5√5)2n(11)1 - 2n+1C2(5√5)2n−1(11)2.......... ..............(2)
(1) - (2) gives
(5√5+11)2n+1 - (5√5−11)2n+1 = 2[2n+1C1(5√5)2n(11)1 + 2n+1C2(5√5)2n−1(11)2..............]
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