How do you find the numerically greatest coefficient?
To Find the greatest coefficient in the expansion of (1+x)n. The coefficient of the general term (1+x)nisnCr and we have to find value of r for which this is greatest. When n is even, the greatest coefficient is nCn/2. when n is odd, the greatest coefficient is nCn−1/2ornCn+1/2 ; these two coefficients being equal.
What is greatest binomial coefficient?
But r must be an integer, and therefore when n is even, the greatest binomial coefficient is given by the greatest value of r, consistent with (1) i.e., r = n/2 and hence the greatest binomial coefficient is nCn/2. …
What is the expansion of a B n?
If a and b are real numbers and n is a positive integer, then (a + b)n =nC0 an + nC1 an – 1 b1 + nC2 an – 2 b2 + 1. The total number of terms in the binomial expansion of (a + b)n is n + 1, i.e. one more than the exponent n.
Which term is 2x 3y 12?
8th term
8th term.
What is the expansion of E X?
(Math | Calculus | Series | Exponent)
| Function | Summation Expansion | Comments |
|---|---|---|
| e | e= 1 / n! = 1/1 + 1/1 + 1/2 + 1/6 + … | see constant e |
| e -1 | = (-1) n / n! = 1/1 – 1/1 + 1/2 – 1/6 + … | |
| e x | = xn / n! = 1/1 + x/1 + x2 / 2 + x3 / 6 + … |
What is the expansion of X Y N?
This information can be summarized by the Binomial Theorem: For any positive integer n, the expansion of (x + y)n is C(n, 0)xn + C(n, 1)xn-1y + C(n, 2)xn-2y2 + + C(n, n – 1)xyn-1 + C(n, n)yn. Each term r in the expansion of (x + y)n is given by C(n, r – 1)xn-(r-1)yr-1. Example: Write out the expansion of (x + y)7.
How do you find the number of rational terms?
The number of rational terms in the expression of (a1/l + b1/k )n is [n / LCM of {l,k}] when none of and is a factor of and when at least one of and is a factor of is [n / LCM of {l,k}] + 1 where [.] is the greatest integer function. Illustration: Find the number of irrational terms in (8√5 + 6√2)100.
What is the expansion of E 2?
Well, we already know the answer is e2 = 2.71828… × 2.71828… = 7.389056…
What is series for E X?
So the Maclaurin series is: ex=1+1×0!
How do you find the numerically greatest term in binomial expansion?
Numerically greatest term in the binomial expansion: p=∣x∣+1(n+1)∣x∣. Numerically greatest term in the expansion of ( 1 + x ) n (1+x)^n (1+x)n is T c + 1 T_{c+1} Tc+1, if ( n + 1 ) ∣ x ∣ ∣ x ∣ + 1 \frac{(n+1)|x|}{|x|+1} ∣x∣+1(n+1)∣x∣ is not an integer, where c = ( n + 1 ) ∣ x ∣ ∣ x ∣ + 1 . c=\frac{(n+1)|x|}{|x|+1} .
How do you expand XYN?
For any positive integer n, the expansion of (x + y)n is C(n, 0)xn + C(n, 1)xn-1y + C(n, 2)xn-2y2 + + C(n, n – 1)xyn-1 + C(n, n)yn. Each term r in the expansion of (x + y)n is given by C(n, r – 1)xn-(r-1)yr-1. Example: Write out the expansion of (x + y)7.
Which term has the greatest coefficient in (x + 1/x) 2n?
Note: The greatest binomial coefficient is the binomial coefficient of the middle term. Illustration: Show that the greatest the coefficient in the expansion of (x + 1/x) 2n is (1.3.5…(2n-1).2 n)/n! . Solution: Since middle term has the greatest coefficient.
Which expansion of (2 + (3/8)x) 10 has the maximum numerical value?
Given that the 4 th term in the expansion of (2 + (3/8)x) 10 has the maximum numerical value, find the range of values of x for which this will be true. Given 4 th term in (2 + (3/8)x) 10 = 2 10 (1 + (3/16)x) 10, is numerically greatest
What is the greatest coefficient of the middle term?
Note: The greatest binomial coefficient is the binomial coefficient of the middle term. Show that the greatest the coefficient in the expansion of (x + 1/x) 2n is (1.3.5… (2n-1).2 n )/n! . Since middle term has the greatest coefficient. So, greatest coefficient = coefficient of middle term
What is the greatest binomial coefficient when n is even?
(1) But r must be an integer, and therefore when n is even, the greatest binomial coefficient is given by the greatest value of r, consistent with (1) i.e., r = n/2 and hence the greatest binomial coefficient is n C n/2.
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