# Greatest Term in Binomial Expansion

In general to locate maximum term in the expansion (1 +

*x*)*we find the value of*^{n}*r*till the ratio*T*_{r}_{+1}/*T*is greater than 1 as for this value of_{r}*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, letâ‡’

*r*â‰¤Then the greatest term occurs for

*r*= = integral part of If is an exact integer then*T*and_{r}*T*_{r}_{+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**The greatest coefficient in the binomial expansion is equivalent to the greatest term when**

*Note:**x*= 1.