Algebra-Binomial Theorem

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solution Expand (2x+3y)^5\,

solution Find the fourth term in (\frac{3}{x}+y)^7\,

solution Find the middle term of the expansion (\frac{x}{y}+\frac{y}{x})^8\,

solution Find the middle terms of the expansion of (3x+\frac{1}{2x})^7\,

solution Find the constant term in the expansion of (3x-\frac{5}{x^2})^9\,

solution Find the independent term of x\, in the expansion of (x-\frac{1}{x})^6\,

solution Find the independent term of x\, in the expansion of (6x^2-\frac{5}{x^2})^6\,

solution Find the coefficient of x^3\, in the expansion of (3x+4)^6\,

solution Find the fifth term in the expansion of (2x+\frac{1}{3y})^8\,

solution Prove that {C \choose 0}+{C \choose 2}+{C \choose 4}+...=2^{n-1}={C \choose 1}+{C \choose 3}+{C \choose 5}+.......\,

solution Prove that ({C \choose 0})^2+({C \choose 1})^2+({C \choose 2})^2+......+({C \choose n})^2=\frac{(2n)!}{(n!)^2}\,

solution Show that 676\, divides 3^{3n}-26n-1\,, where n\,is an integer.

solution If (1+x)^n={C \choose 0}+{C \choose 1}x+{C \choose 2} x^2+.......+{C \choose n} x^n\, then show that 1{C \choose 0}+2{C \choose 1}+3{C \choose 2}+........+(n+1){C \choose n}\,

solution Find the term containing x^5\, in the expansion of (x-\frac{1}{x})^{11}\,

solution In the expansion of (1+a)^n\, if the coefficient of a^{r-1},a^r,a^{r+1}\, are in AP.then prove that n^2-n(4r+1)+4r^2-2=0\,

solution Find the value of (0.99)^9\, corrected to 4 decimals using the binomial theorm.

solution Prove that {C \choose 1}^{2}-2{C \choose 2}^{2}+3{C \choose 3}^{2}-.....+2n {C \choose 2n}^2=(-1)^{n-1}n{C \choose 0}\,

solution Find the sum of the coefficients of the even powers of x in the expansion of (1+x+x^2+x^3)^5\,

solution Prove that 2{C \choose 0}+2^2 \frac{{C \choose 1}}{2}+2^3 \frac{{C \choose 2}}{3}+......+2^{n+1}\frac{{C \choose n}}{n+1}=\frac{3^{n+1}-1}{n+1}\,

solution Prove that {C \choose 0}+\frac{{C \choose 1}}{2} x+\frac{{C \choose 2}}{3} x^2+.....+\frac{{C \choose n}}{n+1} x^n=\frac{(1+x)^{n+1}-1}{(n+1)x}\,


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