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Greatest Term in Binomial Expansion

In general to locate maximum term in the expansion (1 + x)n we find the value of r till the ratio Tr+1/Tr is greater than 1 as for this value of r any term is always greater than its previous term. The value of r till this occurs gives the greatest term. So for greatest term, let
Then the greatest term occurs for r = 67080.png = integral part of 67074.pngIf 67068.png is an exact integer then Tr and Tr+1 both are the greatest terms.
When we have expansion in which positive and negative signs occur alternatively we find numerically the greatest term (ignoring the negative value) for which we find the value of r considering ratio 67062.png
Note: The greatest coefficient in the binomial expansion is equivalent to the greatest term when x = 1.

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