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find the value of x in the expansion of (1+x)^44

if the 21st and 22nd terms in the expansion of (1+x)^44 are equal. Find the value of x 

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Robert J. | Certified High School AP Calculus and Physics TeacherCertified High School AP Calculus and Ph...
4.6 4.6 (13 lesson ratings) (13)
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By binomial expansion, if the 21st and 22nd terms are equal, then

C(44, 20) x^24 = C(44, 21) x^23

Solve for x,

x = C(44, 21)/C(44, 20) = 8/7 <==Answer

 

Comments

C(44, 20) x^24 = C(44, 21) x^23

For the 20th and 21 st term, it should read, C(44, 20) x^20 = C(44, 21) x^21

44! X^20                              44! X^21

------------------------ = ---------------------------

24! 20!                                  23! 21!

 

23! 21 20!

-------------- = x = 7/8  (the reciprocal)

24 23! 20!

Not possible to edit comment.  It should read the 21st and 22nd term.