If the sum to infinity of the series `1+2r+3r^2+4r^3+`is 9/4, then val – InterviewSolution

InterviewSolution

1.	If the sum to infinity of the series `1+2r+3r^2+4r^3+`is 9/4, then value of `r`is`1//2`b. `1//3`c. `1//4`d. none of theseA. `1//2`B. `1//3`C. `1//4`D. none of these
Answer» Correct Answer - B `S=1+2r+3r^(2)+4r^(3)+..` `thereforerS=r+2r^(2)+3r^(3)+4r^(4)+..` `rArr(1-r)S=1+r+r^(2)+r^(3)+..` `=1/(1-r)` `rArrS=1/((1-)^(2))` Given `S=9/4` `rArr1/((1-r)^(2))=9/4` `rArr1-r=pm2/3` `rArrr=1/3or5/3` Hence, r=1/3 as `0ltabsrlt1`

Discussion

No Comment Found

Related InterviewSolutions

Let `f(n)` denote the `n^(th)` terms of the seqence of `3,6,11,18,27,….` and `g(n)` denote the `n^(th)` terms of the seqence of `3,7,13,21,….` Let `F(n)` and `G(n)` denote the sum of `n` terms of the above sequences, respectively. Now answer the following: `lim_(ntooo)(f(n))/(g(n))=`A. `0`B. `1`C. `2`D. `oo`
Let `f(n)` denote the `n^(th)` terms of the seqence of `3,6,11,18,27,….` and `g(n)` denote the `n^(th)` terms of the seqence of `3,7,13,21,….` Let `F(n)` and `G(n)` denote the sum of `n` terms of the above sequences, respectively. Now answer the following: `lim_(ntooo)(F(n))/(G(n))=`A. `2`B. `1`C. `0`D. `oo`
Find the sum of the series `1^2+3^2+5^2+ ton`terms.
The 15th term of the series `2 1/2+1 7/(13)+1 1/9+(20)/(23)+..` isA. `10/39`B. `10/21`C. `10/23`D. none of these
If the first two terms of a H.P. are `2//5and12//23` respectively. Then, largest term is
Let `a_(1),a_(2),a_(3), . . .` be a harmonic progression with `a_(1)=5anda_(20)=25`. The least positive integer n for which `a_(n)lt0`, isA. 22B. 23C. 24D. 25
If `Sigma_(r=1)^(50) (2)/(r^2+(11-r^2))`, then the value of n is __________
`Sigma_(r=1)^(50)(r^2)/(r^2+(11-r)^2)` is equal to ______.
The value of the sum `Sigma_(i=1)^(20) i(1/i+1/(i+1)+1/(i+2)+.....+1/(2))` is ______________.
Find the sum of series upto n terms `((2n+1)/(2n-1))+3((2n+1)/(2n-1))^2+5((2n+1)/(2n-1))^3+...`