यदि `(1+x)^(n)` के विस्तार में `a_(1),a_(2),a_(3),a_(4)` किन्हीं चार क्रमागत पदों के गुणांक हों, तो सिद्ध कीजिए कि
`(a_(1))/(a_(1)+a_(2))+(a_(3))/(a_(3)+a_(4))=(2a_(2))/(a_(2)+a_(3))`

,1+a_(1),a_(2),a_(3)a_(1),1+a_(2),a_(3)a_(1),a_(2),1+a_(3)]|=0, then

If the coefficients of 4 consecutive terms in the expansion of (1+x)^(n) are a_(1),a_(2),a_(3),a_(4) respectively, then show that (a_(1))/(a_(1)+a_(2))+(a_(3))/(a_(3)+a_(4))=(2a_(2))/(a_(2)+a_(3))

If the coefficients of 4 consecutive terms in the expansion of (1+x)^(n) are a_(1),a_(2),a_(3),a_(4) respectively, then show that (a_(1))/(a_(1)+a_(2))+(a_(3))/(a_(3)+a_(4))=(2a_(2))/(a_(2)+a_(3))

If the coefficients of the consicutive four terms in the expansion of (1+x)^(n)" be "a_(1),a_(2),a_(3)and a_(4) respectively , show that , (a_(1))/(a_(1)+a_(2))+(a_(3))/(a_(3)+a_(4))=2.(a_(2))/(a_(2)+a_(3)).

If a_(1),a_(2),a_(3),a_(4) be the coefficient of four consecutive terms in the expansion of (1+x)^(n), then prove that: (a_(1))/(a_(1)+a_(2))+(a_(3))/(a_(3)+a_(4))=(2a_(2))/(a_(2)+a_(3))

If a_(1),a_(2),a_(3),,a_(n) are an A.P.of non-zero terms, prove that _(1)(1)/(a_(1)a_(2))+(1)/(a_(2)a_(3))++(1)/(a_(n-1)a_(n))=(n-1)/(a_(1)a_(n))

If a_(1), a_(2) , a_(3),…,a _(n+1) are in A. P. then the value of (1)/(a _(1)a_(2))+(1)/(a_(2)a_(3))+(1)/(a_(3)a_(4))+...+(1)/(a_(n)a_(n+1)) is-

If |(1+a_(1),a_(2),a_(3)),(a_(1),1+a_(2),a_(3)),(a_(1),a_(2),1+a_(3))|=0 then a_(1)+a_(2)+a_(3)=