সাধারণ পদ , মধ্যপদ ও সমদূরবর্তী পদ নির্ণয়
Find ;7th7^{th}7th term of (4x5−52x)9\displaystyle \left ( \frac{4x}{5}-\frac{5}{2x} \right )^{9}(54x−2x5)9
10050x3\dfrac{10050}{x^{3}}x310050
10500x3\dfrac{10500}{x^{3}}x310500
1050x3\dfrac{1050}{x^{3}}x31050
1000x3\dfrac{1000}{x^{3}}x31000
7th7^{th}7th term of (4x5−52x)9\displaystyle \left ( \frac{4x}{5}-\frac{5}{2x} \right )^{9}(54x−2x5)9
T6+1=9C6(4x5)9−6(−52x)6\displaystyle T_{6+1}=^{9}\textrm{C}_{6}\left ( \frac{4x}{5} \right )^{9-6}\left ( -\frac{5}{2x} \right )^{6}T6+1=9C6(54x)9−6(−2x5)6
=9!3!6!(4x5)3(52x)6=10500x3\displaystyle =\frac{9!}{3!6!}\left ( \frac{4x}{5} \right )^{3}\left ( \frac{5}{2x} \right )^{6}=\frac{10500}{x^{3}}=3!6!9!(54x)3(2x5)6=x310500
The total number of rational terms in the expansion of (713+1119)6561\left(7^{\frac 13} + 11^{\frac 19}\right)^{6561}(731+1191)6561 is
The number of irrational terms in the expansion of(58+26)100,( \sqrt [ 8 ] { 5 } + \sqrt [ 6 ] { 2 } ) ^ { 100 } ,(85+62)100, is
In the expansion of (a−b)n,n≥5(a-b)^{n},n\ge 5(a−b)n,n≥5, if the sum of the 5th5^{th}5th and 6th6^{th}6th terms is zero, then a/ba/ba/b=
The middle term in the expansion of (1−3x+3x2−x3)6(1-3x+3x^{2}-x^{3})^{6}(1−3x+3x2−x3)6 is
