Home
Class 12
MATHS
If 1-1/3+1/5-1/7+1/9-1/(11)+=pi/4 , then...

If `1-1/3+1/5-1/7+1/9-1/(11)+=pi/4` , then value of `1/(1xx3)+1/(5xx7)+1/(9xx11)+` is `pi//8` b. `pi//6` c. `pi//4` d. `pi//36`

A

`pi//8`

B

`pi//6`

C

`pi//4`

D

`pi//36`

Text Solution

Verified by Experts

The correct Answer is:
A
We have
`pi/4=(1-1/3)+(1/5-1/7)+(1/9-1/11)+…`
`=2/(1xx3)+2/(5xx7)+2/(9xx11)+..`
`rArr1/(1xx3)+1/(5xx7)+1/(9xx11)+..=pi/8`
Promotional Banner

Topper's Solved these Questions

  • PROGRESSION AND SERIES

    CENGAGE ENGLISH|Exercise EXERCIESE ( LINKED COMPREHENSION TYPE )|60 Videos

  • PROGRESSION AND SERIES

    CENGAGE ENGLISH|Exercise EXERCIESE ( NUMERICAL VALUE TYPE )|28 Videos

  • PROGRESSION AND SERIES

    CENGAGE ENGLISH|Exercise CONCEPT APPLICATION EXERICISE 5.9|9 Videos

  • PROBABILITY II

    CENGAGE ENGLISH|Exercise MULTIPLE CORRECT ANSWER TYPE|6 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE ENGLISH|Exercise Archives (Numerical Value Type)|3 Videos

Similar Questions

Explore conceptually related problems

The value of 1/(log_3pi)+1/(log_4pi) is

The value of sin^(-1)(-sqrt(3)//2)\ is- a. -pi//3 b. -2pi//3 c. 4pi//3 d. 5pi//3

The value of int_0^pi1/(5+3cosx)dx is a. pi//2 b. pi//4 c. 0 d. pi//8

The value of cos^(-1)(-1)-sin^(-1)(1) is: a. pi b. pi/2 c. (3pi)/2 d. -(3pi)/2

int_1^(sqrt(3))1/(1+x^2)dx is equal to a. pi/(12) b. pi/4 c. pi/6 d. pi/3

The value of sin^(-1)(cos((33pi)/5)) is (a) (3pi)/5 (b) -pi/(10) (c) pi/(10) (d) (7pi)/5

The value of sin^(-1)(cos(33pi)/5) is (a) (3pi)/5 (b) -pi/(10) (c) pi/(10) (d) (7pi)/5

The value of cos((2pi)/7)cos((4pi)/7)cos((6pi)/7) is a. -1//2 b. \ 1//2 c. \ 1//4 d. 1//8

The value of tan^(-1)(1)+cos^(-1)(-1/2)+sin^(-1)(-1/2) is equal to pi/4 b. (5pi)/(12) c. (3pi)/4 d. (13pi)/(12)

The principal value of the amplitude of (1+i) is A. pi B. pi/(12) C. pi/4 D. (3pi)/4

CENGAGE ENGLISH-PROGRESSION AND SERIES-EXERCIESE ( SINGLE CORRECT ANSWER TYPE )
  1. Consider the sequence 1,2,2,4,4,4,4,8,8,8,8,8,8,8,8,... Then 1025th te...

    Text Solution

    |

  2. The value of sum(i-1)^nsum(j=1)^isum(k=1)^j1=220 , then the value of n...

    Text Solution

    |

  3. If 1^2+2^2+3^2++2003^2=(2003)(4007)(334) and (1)(2003)+(2)(2002)+(3)(2...

    Text Solution

    |

  4. If tn denotes the nth term of the series 2+3+6+11+18+….. Then t50 is

    Text Solution

    |

  5. The sum of series Sigma(r=0)^(r) (-1)^r(n+2r)^2 (where n is even) is

    Text Solution

    |

  6. If (1^2-t1)+(2^2-t2)+---+(n^2-tn)=(n(n^2-1))/3 , then tn is equal to a...

    Text Solution

    |

  7. If (1+3+5++p)+(1+3+5++q)=(1+3+5++r) where each set of parentheses cont...

    Text Solution

    |

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

    Text Solution

    |

  9. The sum to 50 terms of the series 3/1^2+5/(1^2+2^2)+7/(1^+2^2+3^2)+...

    Text Solution

    |

  10. Let S=4/(19)+(44)/(19^2)+(444)/(19^3)+ u ptooo . Then s is equal to a....

    Text Solution

    |

  11. If 1-1/3+1/5-1/7+1/9-1/(11)+=pi/4 , then value of 1/(1xx3)+1/(5xx7)+1/...

    Text Solution

    |

  12. If 1/(1^2)+1/(2^2)+1/(3^2)+ tooo=(pi^2)/6,t h e n1/(1^2)+1/(3^2)+1/(5^...

    Text Solution

    |

  13. lim(nrarroo) Sigma(r=1)^(n) (r)/(1xx3xx5xx7xx9xx...xx(2r+1)) is equal ...

    Text Solution

    |

  14. The greatest interger by which 1+Sigma(r=1)^(30) rxxr ! is divisible...

    Text Solution

    |

  15. If Sigma(r=1)^(n) r^4=I(n), " then "Sigma(r=1)^(n) (2r -1)^4 is equal ...

    Text Solution

    |

  16. Value of lim(ntooo)(1+1/3)(1+1/(3^2))(1+1/(3^4))(1+1/(3^8))oo is equal...

    Text Solution

    |

  17. If x1,x2 …,x(20) are in H.P and x1,2,x(20) are in G.P then Sigma(r=1)^...

    Text Solution

    |

  18. The value of Sigma(r=1)^(n) (a+r+ar)(-a)^r is equal to

    Text Solution

    |

  19. The sum of series x/(1-x^2)+(x^2)/(1-x^4)+(x^4)/(1-x^8)+ to infinite t...

    Text Solution

    |

  20. The sum of 20 terms of the series whose rth term s given by kT(n)=(-1)...

    Text Solution

    |