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Lecture - 6 Chapter 8 Binomial Theorem
| NCERT Examples |
Example 4. Using binomial theorem, prove that 6^n-5n always leaves remainder 1 when divided by 25.
Example 6. Show that the middle term in the expansion of (1+x)^{2n} is \frac{1.3.5…(2n-1)}{n!} 2^n . x^n, where n is a positive integer.
Example 10. Find the term independent of x in the expansion of \left ( \frac{3}{2}x^2 – \frac{1}{3x} \right )^6.
Example 11. If the coefficients of a^{r-1}, a^r \text{ and } a^{r+1} in the expansion of (1+a)^n are in arithmetic progression, prove that n^2-n(4r+1)+4r^2-2=0.
Example 12. Show that the coefficient of the middle term in the expansion of (1+x)^{2n} is equal to the sum of the coefficients of two middle terms in the expansion of (1+x)^{2n-1} .
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Example 14. Find the rth term from the end in the expansion of (x+a)^n.
Example 15. Find the term independent of x in the expansion of \left ( \sqrt[3]{x} +\frac{1}{2 \sqrt[3]{x}} \right )^{18} , x>0.
Example 16. The sum of the coefficients of the first three terms in the expansion of \left ( x – \frac{3}{x^2} \right )^m, x \ne 0, m being a natural number, is 559. Find the term of the expansion containing x^3.
Example 17. If the coefficients of (r-5)^{th} and (2r-1)^{th} terms in the expansion of (1+x)^{34} are equal, find r.
