The middle term in the expansion of x+1/x 10
WebExpand Using the Binomial Theorem (x+1)^10 (x + 1)10 ( x + 1) 10 Use the binomial expansion theorem to find each term. The binomial theorem states (a+b)n = n β k=0nCkβ
(anβkbk) ( a + b) n = β k = 0 n n C k β
( a n - k b k). 10 β k=0 10! (10β k)!k! β
(x)10βk β
(1)k β k = 0 10 10! ( 10 - k)! k! β
( x) 10 - k β
( 1) k Expand the summation. WebSep 26, 2014 Β· We can see that the general term becomes constant when the exponent of variable x is 0. Therefore, the condition for the constant term is: n β 2k = 0 β k = n 2 . In other words, in this case, the constant term is the middle one ( k = n 2 ).
The middle term in the expansion of x+1/x 10
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WebFind the tenth term in the expansion of (x + 3)12. To find the tenth term, I plug x, 3, and 12 into the Binomial Theorem, using the number 10 β 1 = 9 as my counter: 12C9 ( x) 12β9 (3) β¦ WebThe expansion of (1+x)^10 contains 10+1 = 11 terms. Hence 6th term is the middle term. Formula for general term in the binomial expansion is given by Tr+1 = nCr a^n-r b^r r+1 = 6 β¦
WebThe term independent of x in the expansion of x + 1 x 2 3 - x 1 3 + 1 - x - 1 x - x 1 2 10, x β 1, is equal to Solution Step 1: Simplify the given expression: Given expression is x + 1 x 2 3 - x 1 3 + 1 - x - 1 x - x 1 2 10 and x β 1. The above expression can be simplified as follows WebThe general term of the binomial expansion of (x + y)^n is Tr+1 = nCr x^n-y^ (n-r) View the full answer Final answer Transcribed image text: Find the middle term in the expansion of (x9 + 9x)10. The middle term of (x9 + 9x)10 is . (Simplify your answer.) Use the Binomial Theorem to expand the binomial. (5x+ 1)4 (5x+ 1)4 = (Simplify your answer.)
WebMar 30, 2024 Β· (2π β 1))/π! 2n xn, where n is a positive integer. Given Number of terms = 2n which is even So, Middle term = (2n/2 + 1)th term = (n + 1)th term Hence, we need to find β¦ WebAnswer (1 of 2): It is good if you do not have to rely on formulas to do stuff like this. If you know how to expand these binomial series it is no big deal! Watch this simple method: It does not matter if you need to write the 3 or 4 terms leading up to the one you are wanting. It β¦
WebExpand Using the Binomial Theorem (x+1)^10 (x + 1)10 ( x + 1) 10 Use the binomial expansion theorem to find each term. The binomial theorem states (a+b)n = n β β¦
WebThe number of terms in the expansion is (n + 1), which is even. Hence, there are two middle terms and they are given by T(n + 1)/2 and T(n + 3)/2 Examples Example 1 : Find the β¦ dsc railwayWebAug 24, 2024 Β· Best answer Given, expansion is (x β 1 x)2n ( x - 1 x) 2 n. This Binomial expansion has even power. So, this has one middle term. i.e., ( 2n 2 + 1) ( 2 n 2 + 1) th term = (n + 1)th = ( n + 1) t h term T n+1 =.2n C n(x)2nβn( β 1 x)n =.2n C nxn( β 1)n xβn T n + 1 =. 2 n C n ( x) 2 n - n ( - 1 x) n =. 2 n C n x n ( - 1) n x - n commercial grade shopping cartWebMiddle Term = [ (6n/2) + 1] term = 6nC 3n (βx) 3n Determining a Particular Term: In the expansion of (ax p + b/x q) n the coefficient of x m is the coefficient of T r+1 where r = [ (npβm)/ (p+q)] In the expansion of (x + a) n, T r+1 /T r = (n β r + 1)/r . a/x General and Middle Terms of Binomial Expansion 1,577 Independent Term commercial grade shower curtain linerWebJan 30, 2024 Β· The binomial theorem states the principle of expanding an algebraic expression of the form \ ( (a+b)^ {n}\) and expresses it as a sum of the terms involving individual exponents of the variables, \ (a\) and \ (b\) \ ( {\left ( {a + b} \right)^n} = \sum\limits_ {k = 0}^n { {}^n {C_k} {a^ {n β k}} {b^k}} \) dscr assured supplier listWebQuestion The coefficient of middle term in the expansion of (1+x) 10 is A 10!/ 5!6! B 10!/5! 2 C 10! 5! 7! D None of these Medium Solution Verified by Toppr Correct option is B) (1+x) β¦ dsc red clayWebJul 26, 2024 Β· Best answer Show that the term independent of x in the expansion of (x β 1 x)10 ( x β 1 x) 10 is - 252. Formula Used: General term, Tr+1 of binomial expansion (x + y)n is given by, Now, finding the general term of the expression, (x β 1 x)10 ( x β 1 x) 10 , we get Tr+1 = 10C1 x x10-r x ( β1 x)r ( β 1 x) r commercial grade shower curtain rodWebMay 10, 2024 Β· The middle terms in the expansion of `(x+(1)/(x))^(10)` is- dscr chart