show that the coefficient of middle term in the expansion of (1+x)8 is equal to the term of the coefficients of middle teema in the expansion of (1+a)7

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Solution

Dear student

$(1 + x)^{8} t h e r e a r e (8 + 1) = 9 t e r m s m i d d l e t e r m = 5 t h t e r m =_{4}^{8} C x^{4} c o e f f i c i e n t =_{4}^{8} C = \frac{8!}{4! 4!} = 70 (1 + a)^{7} t h e r e a r e (7 + 1) = 8 t e r m s m i d d l e t e r m = 3 r d t e r m a n d 4 t h t e r m =_{3}^{7} C a^{3} +_{4}^{7} C a^{4} c o e f f i c i e n t = =_{3}^{7} C +_{4}^{7} C = \frac{7!}{3! 4!} + \frac{7!}{4! 3!} = 35 + 35 = 70$

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