binomial expansion Watch

bl64
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#1
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Find the first 3 terms of the expansion in ascending powers of x

(x+ 1/x)6

I thought this would be x6 + 6x4 +15x2 given that the expansion would be 1a6 + 6a5b+15a4b2

However the answer book gave me 1/x6 + 6/x4 + 15/x2

Is the book wrong or have I mucked up my working?
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shawn_o1
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(x+1/x)6 = x6(1+(1/x)2)6

Use the expansion of (1+x)n
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brianeverit
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(Original post by bl64)
Find the first 3 terms of the expansion in ascending powers of x

(x+ 1/x)6

I thought this would be x6 + 6x4 +15x2 given that the expansion would be 1a6 + 6a5b+15a4b2

However the answer book gave me 1/x6 + 6/x4 + 15/x2

Is the book wrong or have I mucked up my working?
You have found the expansion in descending powers of x. the question wanted ascending powers.
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gdunne42
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(Original post by bl64)
Find the first 3 terms of the expansion in ascending powers of x

(x+ 1/x)6

I thought this would be x6 + 6x4 +15x2 given that the expansion would be 1a6 + 6a5b+15a4b2

However the answer book gave me 1/x6 + 6/x4 + 15/x2

Is the book wrong or have I mucked up my working?
The answer you have given is the last 3 terms in descending powers of x
Try expanding (1/x + x)^6


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