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If the sum to infinity of the series `1+2r+3r^2+4r^3+` is 9/4, then value of `r` is (a)`1//2` b. `1//3` c. `1//4` d. none of these

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CENGAGE ENGLISH-SEQUENCES AND SERIES-All Questions
  1. Let S=4/(19)+(44)/(19^2)+(444)/(19^3)+ u ptooo . Then s is equal to a....

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  2. If Hn=1+1/2+...+1/ndot , then the value of Sn=1+3/2+5/3+...+(99)/(50) ...

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

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  4. The sum o f series 1+4/5+7/(5^2)+(10)/(5^3)+oo is a. 7//16 b. 5//16 ...

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  5. The sum 20 terms of a series whose rth term is given by Tr=(-1)^r((r^2...

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  6. Consider the sequence 1,2,2,4,4,4,4,8,8,8,8,8,8,8,8,... Then 1025th te...

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  7. If a ,1/b ,c and1/p ,q ,1/r form two arithmetic progressions of the c...

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  8. Suppose that F(n+1)= (2F(n)+1)/2 'for n=1,2,3 a n dF(1)=2. T h e ndot...

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  9. In an A.P. of which a is the first term if the sum of the first p term...

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  10. If Sn denotes the sum of first n terms of an A.P. and (S(3n)-S(n-1))/(...

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  11. If a ,b ,and c are in A.P., then a^3+c^3-8b^3 is equal to (a).2a b c (...

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  12. The number of terms of an A.P. is even. The sum of the odd terms is 24...

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  13. The largest term common to the sequences 1, 11 , 21 , 31 ,...... to 10...

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  14. If the sum of m terms of an A.P. is the same as the sum of its n terms...

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  15. If Sn denotes the sum of n terms of A.P., then S(n+3)-3S(n+2)+3S(n+1)...

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  16. About 150 workers were engaged to finish a piece of work in a certain ...

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  17. in a G.P (p+q)th term = m and (p-q) th term = n , then find its p th t...

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  18. Assertion: There are infinite geometric progressions of for which 27,8...

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  19. If A1, A2, G1, G2, ; a n dH1, H2 are two arithmetic, geometric and har...

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  20. Let S(1),S(2),"…." be squares such that for each n ge 1, the length o...

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