In the expansion of a binomial (a+b)^n the third term is equal to 56/9, the fourth term is 70/3, and the binomial coefficients of the third and the sixth term are equal. Find the values of a, b, and n
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m=1/2
Given (1+x)m
third term is 8−1x2
For (1+x)n the expansion is:
(1+x)n=1+nx+2!n(n−1)x2+....
So, the third term in (1+x)m is 2!m(m−1)x2
Solving:
=2m(m−1)x2=8−1x2
=2m(m−1)=8−1
=(m−1)=4−1
=m2−m+41=0
=4m2−4m+1=0
=(2m−1)2=0
∴ m=2
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