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Find the term independent of x in the expansion of (2x - 1/x)10
the second, third and fourth term of the binomial expansion (x+a)n (n is actually (x+a)raised to the power n) are 240, 720 and 1080. find x, a and n.
If the coeffients of 5th, 6th & 7th terms in expansion of (1+x)n are in AP, then find values of n???
the coefficient of x4 in the expansion of (1+x+x2+x3)11 is :
a) 900 b)909
c) 990 d)999
If 3rd,4th,5th,6th term in the expansion of (x+alpha)n be respectively a,b,c and d, prove that b2-ac/c2-bd=4a/3c..
if 4th term in the expansion of ( ax+1/x)n is 5/2, then the values of a and n :
a) 1/2,6 b) 1,3
The coefficients of three consecutive terms in the expansion of(1+x)n are in the ratio 1:7:42. find n.
Show that the middle term in the expansion of(1+x)raise to power 2n is = 1.3.5.......(2n-1) . 2n.xraise to power n upon n! , where nis a +ve integer.
Using Binomial theoram, prove that 23n - 7n-1 is divisible by 49 where n is a Natural number
if the coefficients of (r-5)th and (2r-1)th term in the expansion of (1+x)34 are equal, fiind r
Show that C0/2 + C1/3 + C2/4 + ......... + Cn/n+2 = (1+n.2(n+1))/(n+1)(n+2)
Please tell me the answer to this question. Need urgently. Help from meritnation experts would be commendable . Please help !
in the second example, just by finding n2=9, we can conclude that n=3. so why did we have to find n3=27?
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 (1+x)^2n-1.
using binomial therorem, 32n+2-8n-9 is divisible by 64, n belongs to N
Find the value of nC0 - nC1 + nC2 - nC3 +.................+(-1)^n nCn
if three successive coefficients in the expressions of (1+x)n are 220, 495 and 792 respectively, find the value of n?
Using binomial theoram ,show that 9n+1-8n-9 is divisible by 64 ,whr n is a positive integer.
and n in
the expansion of (a
if the first three terms of the expansion are 729, 7290 and 30375,
n, if the
ratio of the fifth term from the beginning to the fifth term from the
end in the expansion of
Find the sixth term of the expansion (y1/2 + x1/3)n, if the binomial coefficient of the third term from the end is 45.
the first three terms in the expansion of (x+y)^n are 1,56,1372 respectively.Find x and y
prove nPr= n!
and deduce it to nCr answere fast important for test
If (1+x)n= C0 + C1x + C2x2+ …..+Cnxn. Prove that C1 + 2C2 + 3C3 + ……+ nCn = n.2n-1
The cofficient of three consecutive terms in the expansion of (1+x)nare in the ratio 1:7:42.find n?
prove that nCr +nCr-1 = n+1Cr
The sum of the coefficients of the first three terms in the expansion of (x-3/x2)m , x is not equal to 0,m being a natural number, is 559. Find the term of the wxpansion containing x3. (NCERT PG 174 EXAMPLE NO 16). The steps in the NCERTbook are not clear..
The 3rd, 4th and 5th terms in the expansion of (x + a)n are respectively 84, 280 and 560, find the values of x, a and n.
find the [n+1]th term from the end in the expansion of [x-1/x]^3n
the coefficients of 2nd, third and fourth terms in the expansion of (1+n)^2n are in AP.Prove that 2n^2-9n+7=0
please explain the line in ex 3 - on comparing the indices of x in x2 and tr+1 , we obtain r=4.........
if C1, C2, c3, C4 are the coefficient of 2nd, 3rd , 4th , and 5th , term in the expansion of (1+x)raise to "n" then prove that
C1/C1+c2 + c3/c3+c4 = 2c2/c2+c3 ((((((((((((((((((((( where c1+c2 , c3 +c4 and c2 + c3 are together under the division THAT IS C1 BY C1 +C2 etc.))))))))))))
1. Find the coefficient of x^3in(√(x^5 )+3/√(x^3))^6
in the binomial expansion of (a + b)n , the coefficient of the 4th and the 13th terms are equal to each other. find n?
the coefficients of x^2y^2,yzt^2 and xyzt in the expansion of (x+y+z+t)^4 are in the ratio
(a) 4:2:1 (b)1:2:4
Find the coefficient of x3 in ( root x5 + 3/ root x3 ) 6
(2) Find rth term from the end in ( x + a) n
This is my doubt:
Find a if the coefficients of x2 and x3 in the expansion of (3+ax)9 are equal.
Thanks a lot. =)
Write the sum of exponents of x and y in the expansion of ( x +y )n ? Also find the number of terms in the expansion?
The sum of two numbers is 6 times their geometric mean show that the numbers are in the ratio (3+2.21/2):(3-2.21/2)
Show that 24n-15n-1 is divisible by 225 by using binomial theorem.
using binomial theorem prove that 6n-5n always remender -1when divided by 25
Find the fifth term from the end in the expansion of (x3/2 - 2/x2)9
any 3 successive coefficient in the expansion of (1+x)^n where n is a positive integer are 28,56,70 then n is
please give the blueprint of annual examination of maths paper.
1) C1+2C2+3C3+--------+nCn=n2 to power n-1
if the 21st and 22nd terms in the expansion of (1+x)^44 are equal then find the value of x.
The no of irrational terms in the expansion of (41/5 + 71/10)45 are??????
Find the coefficient of x50 in the expansion :
(1+x)1000 + 2x(1+x)999 +3x2(1+x)998+…………………..+1001x1000
1. Find the total no. of terms in the expansion of (x+a)^100 + (x-a)^100after simplification
The first 3 terms in the expansion of (1+ax)n are 1, 12x, 64x2respectively, Find n and 'a' .
If the coefficient of xr in the expansion of (1-x)2n-1 is denoted by ar then prove that ar-1 + a2n-r = 0.
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