WebMar 30, 2024 · Example 10 Find the term independent of x in the expansion of (3/2 𝑥^2 " − " 1/3𝑥)^6,x > 0. Calculating general term We … WebNov 11, 2024 · In the expansion of (a + b) n, the term which is free from the variables is known as the independent term. In the expansion of (a + b) n the general term is given by: Tr + 1 = nCr ⋅ an – r ⋅ br Note: In the expansion of (a + b) n , the rth term from the end is [ (n + 1) – r + 1] = (n – r + 2)th term from the beginning. CALCULATION:

Binomial Expansion - Finding term independent of x - YouTube

WebJun 11, 2024 · Thus, the term independent of x is -3003 × 310 × 25. (v) ( (√x/3) + √3/2x2)10 Given as ( (√x/3) + √3/2x2)10 If (r + 1)th term in the given expression is independent of x. Now, we have: Tr+1 = nCr xn-r ar For this term to be independent of x, we must have (10-r)/2 – 2r = 0 10 – 5r = 0 5r = 10 r = 10/5 = 2 Therefore, the required … WebMay 1, 2024 · In the following expansions find the term independent of x : (i) (x/2 + 2y)^6. asked Apr 30, 2024 in Binomial Theorem by PritiKumari (49.3k points) binomial theorem; class-11; 0 votes. 1 answer. Find the expansion of (1 + x/2 - 2/x)^4, x ≠ 0 using binomial theorem. asked May 1, 2024 in Binomial Theorem by Ruksar03 (47.8k points) binomial … laserosoitin

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WebMar 29, 2024 · Calculating general term of expansion We know that general term of (a + b)n is Tr+1 = nCr (a)n–r . (a)n For general term of expansion (∛𝑥 " + " 1/ (2 ∛𝑥))^18 Putting … WebFind the term independent of x in the expansion (4x3 +1/2 x) raised to the power eight Expert's answer Let given binomial expansion be (a+b)^n (a+b)n General term , T_ {r+1}=\ ^ {n}C_ra^ {n-r}b^r T r+1 = nC ran−rbr =\ ^ {8}C_r (4x^3)^ {8-r} ( {\frac {1} {2x}})^r = 8C r(4x3)8−r(2x1)r Putting power of x=0 x = 0 We get, WebSolution Verified by Toppr Correct option is A) Given term to expand is ( x3x 2− 3x1)6 We know that T r+1= nC ra n−rb r T r+1= 6C r( 23x 2)6−r(3x−1)r = 6C r(23)6−r( 3−1)r(x 12−2r−r) We need to find the term independent of x Power of x is 0 x 12−3r=x 0⇒12−3r=0⇒12=3r⇒r=4 T 4+1= 6C 4(23)6−4( 3−1)4 ⇒ 2!4!6! (2 23 2)2(3 21) = … laserointi