The sum of 1+n(1-1/x)+(n(n+1))/(2!)(1-1/...

The sum of `1+n(1-1/x)+(n(n+1))/(2!)(1-1/x)^2+oo` will be a. `x^n` b. `x^(-n)` c. `(1-1/x)^n` d. none of these

None of these

Text Solution

Verified by Experts

`:.x,y,z`are in GP `" " " "[x,y,zgt1]`
`:.1nx,1ny,1nz` are in AP.
and `2x,4x,6x` are also in AP. `" " " "[xgt1]`
By property,
`2x+1nx,4x+1ny,6x+1nz` are also in AP.
`(1)/(2x+1nx),(1)/(4x+1ny),(1)/(6x+1nz)` are in HP.

Topper's Solved these Questions

COMPLEX NUMBERS AND QUADRATIC EQUATIONS
CENGAGE ENGLISH|Exercise All Questions|886 Videos

Similar Questions

Explore conceptually related problems

In the expansion of [(1+x)//(1-x)]^2, the coefficient of x^n will be a. 4n b. 4n-3 c. 4n+1 d. none of these

Find the sum (x+2)^(n-1)+(x+2)^(n-2)(x+1)^+(x+2)^(n-3)(x+1)^2++(x+1)^(n-1) (x+2)^(n-2)-(x+1)^n b. (x+2)^(n-2)-(x+1)^(n-1) c. (x+2)^n-(x+1)^n d. none of these

The value of (lim)_(n->oo)((n+2)!+(n+1)!)/((n+2)!-(n+1)!) is a. 1 b . -1 c. 0 d. none of these

The value of the determinant of n^(t h) order, being given by |[x, 1, 1...], [1, x, 1...], [1, 1, x...],[... , ... , ...]| is a. (x-1)^(n-1)(x+n-1) b. (x-1)^n(x+n-1) c. (1-x)^(-1)(x+n-1) d. none of these

sum_(n=1)^(oo)(1)/(2n-1)*x^(2n)=

The coefficient of 1//x in the expansion of (1+x)^n(1+1//x)^n is (n !)/((n-1)!(n+1)!) b. ((2n)!)/((n-1)!(n+1)!) c. ((2n)!)/((2n-1)!(2n+1)!) d. none of these

The value of (lim)_(x->oo)(n !)/((n+1)!-(n)!) is a. 1 b . -1 c. 0 d. none of these

("lim")_(xvec1)((1-x)(1-x^2)...(1-x^(2n)))/({(1-x)(1-x^2)...(1-x^n)}^2),n in N ,e q u a l s ^2n P_n (b) ^2n C_n (c) (2n)! (d) none of these

The coefficient of 1//x in the expansion of (1+x)^n(1+1//x)^n is (a). (n !)/((n-1)!(n+1)!) (b). ((2n)!)/((n-1)!(n+1)!) (c). ((2n)!)/((2n-1)!(2n+1)!) (d). none of these

ifint(dx)/(x^2(x^n+1)^(((n-1)/n)) )=-[f(x)]^(1/n)+c ,t h e nf(x)i s (a) (1+x^n) (b) 1+x^(-1) (c) x^n+x^(-n) (d) none of these

CENGAGE ENGLISH-BINOMIAL THEOREM-All Questions

If n is a positive integer, prove that 1-2n+(2n(2n-1))/(2!)-(2n(2n-1)(...
Text Solution
|
Given, sn=1+q+q^2+.....+q^n ,Sn=1+(q+1)/2+((q+1)/2)^2+...+((q+1)/2)^n...
Text Solution
|
The sum of 1+n(1-1/x)+(n(n+1))/(2!)(1-1/x)^2+oo will be a. x^n b. x^(-...
Text Solution
|
sum(k=1)^ook(1-1/n)^(k-1)=>? a.n(n-1) b. n(n+1) c. n^2 d. (n+1)^2
Text Solution
|
The coefficient of x^4 in the expansion of {sqrt(1+x^2)-x}^(-1) in asc...
Text Solution
|
1+1/3x+(1xx4)/(3xx6)x^2+(1xx4xx7)/(3xx6xx9)x^3+------ is equal to a. x...
Text Solution
|
The value of sum(r=1)^(15)(r2^r)/((r+2)!) is (a).((17)!-2^16)/((17)!) ...
Text Solution
|
(n+2)C0(2^(n+1))-(n+1)C1(2^(n))+(n)C2(2^(n-1))-.... is equal to
Text Solution
|
The value of sum(r=0)^(50)(-1)^r((50)Cr)/(r+2) is equal to a . 1/(50x...
Text Solution
|
In the expansion of [(1+x)//(1-x)]^2, the coefficient of x^n will be a...
Text Solution
|
Statement : The sum of coefficient in the expansion of (3^(-x//4)+3^(5...
Text Solution
|
Let n be a positive integer and k be a whole number, klt=2ndot Statem...
Text Solution
|
Statement 1: sum sum(0le ilt j le n)(i/ (.^n ci)+j/(.^ncj)) is equal t...
Text Solution
|
Statement 1: ^m Cr+^m C(r-1)(^nC1)+^mC(r-2)(^n C2)+....+^n Cr=0 , if m...
Text Solution
|
1+(1/4)+((1*3)/(4*8))+((1*4*7)/(4*8*12))+....=
Text Solution
|
If |x|<1,then 1+n((2x)/(1+x))+(n(n+1))/(2!)((2x)/(1+x))^2+...... is eq...
Text Solution
|
Statement 1: If p is a prime number (p!=2), then [(2+sqrt(5))^p]-2^(p+...
Text Solution
|
Statement 1: The total number of dissimilar terms in the expansion of ...
Text Solution
|
Statement 1: In the expansion of (1+x)^(41)(1-x+x^2)^(40), the coeffic...
Text Solution
|
Statement 1: The coefficient of x^n in (1+x+(x^2)/(2!)+(x^3)/(3!)++(x^...
Text Solution
|