Question i. Find the term independent of x in the expansion of . ii. Find the value of a for which there is no term independent of x in the expansion of Solution i. Expression for the general term in the Binomial expansion of is: For the given case: Hence; Since we are looking for the coefficient […]
Question Find the term independent of x in the expansion of . Solution Expression for the general term in the Binomial expansion of is: For the given case: Hence; Since we are looking for the coefficient of the term independent of i.e. , so we can equate Hence, substituting ; Becomes; Hence coefficient of the term independent of i.e. is .
Question The coefficients of and in the expansion of are equal. Find the value of the non-zero constant a. Solution We need to equate the coefficients of and in the expansion of given expression. We are given expression as; Expression for the general term in the Binomial expansion of is: In the given case: Hence; Since we are looking for the coefficients […]
Question i. Find the coefficient of x in the expansion of . ii. Hence find the coefficient of x in the expansion of . Solution i. We are required to find the coefficient of in the expansion of given expression. We are given expression as; Expression for the general term in the Binomial expansion of is: First rewrite […]
Question In the expansion of , the coefficient of x is 5. Find the value of the constant a. Solution We are given expression as; Expression for the general term in the Binomial expansion of is: In the given case: Hence; Since we are looking for the terms with i.e. we can equate; Now we can find the term with; Substituting ; […]
Question The coefficients of and in the expansion of are and respectively. Find the value of . . Solution We can find the coefficients of and in the expansion of given expression. Let us first find the coefficient of in the expansion of . We are given expression as; Expression for the general term in the Binomial expansion of is: First rewrite the […]