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The series 1/(1cdot2)+2/(3cdot4)+3/(5cdo...

The series `1/(1cdot2)+2/(3cdot4)+3/(5cdot6)+... infty`is-

A

Divergent

B

Convergent

C

Oscillatory

D

None of these

Text Solution

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The correct Answer is:
A
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  2. For the geometric series - 1-k+k^2-k^3+..... Which of the following i...

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  3. The series 1/(1cdot2)+2/(3cdot4)+3/(5cdot6)+... inftyis-

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  4. For a positive term series Sigmaan, the radio test states that-

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  5. If un ge u(n+1) ge 0 for all n, then for convergence of the series ove...

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  6. The series 1-2x+ 3x^2 - 4x^3 + 37....,Where 0 lt x lt 1 , is-

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  7. The series 1-1/2+1-3/4+1-7/8+ ...is-

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  8. Which one of the following is false?

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  9. The series 1/(n(log n)^p is divergent if -

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  10. The series Sigma(-1)^n/(n+1)^p is-

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  11. Which of the following series is non absolutely convergent?

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  12. Which one of the following is false?

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  13. If x is positive, then the series:2/3x+ (3/4)^2x^2+(4/5)^3 x^3+...

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  14. The series: x+x^(1+1//2)+x^(1+1//2+1//3)+x^(1+1//2+1//3+1//4)+...is-

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  15. The series a/b +(a(a+1))/(b(b+1))+(a(a+1)(a+2))/(b(b+1)(b+2))+ is...

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  16. Both D alembert's ratio test and Raabe's test are particular cases of ...

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  17. The alternating series u1-u2+u3-u4+...(0 lt un lt n) is convergent, if...

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  18. The series x+ (2^2x^2)/(lfloor 2)+(3^3x^3)/(lfloor3)+(4^4x^4)/(lfloor3...

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  19. The sum of the alternating harmonic series-

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  20. The series x/1+1/2^* x^3/3 + (1 cdot3)/(2cdot4^*)x^5/5+(1cdot3cdot5)/(...

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