What is the binomial expansion of #(2x+1/x)^7 #?

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Answer 1 · 2015-05-26T18:01:33

The 8th row of Pascal's triangle goes:

#1#, #7#, #21#, #35#, #35#, #21#, #7#, #1#

Multiply this by descending powers of 2:

#128#, #64#, #32#, #16#, #8#, #4#, #2#, #1#

To get the sequence:

#128#, #448#, #672#, #560#, #280#, #84#, #14#, #1#

So:

#(2x+1/x)^7#

#=128x^7 + 448x^5 + 672x^3 + 560x + 280/x + 84/x^3 + 14/x^5 + 1/x^7#