Home
Class 11
MATHS
If 1/(1^2)+1/(2^2)+1/(3^2)+ .......=(pi^...

If `1/(1^2)+1/(2^2)+1/(3^2)+ .......=(pi^2)/6,t h e n1/(1^2)+1/(3^2)+1/(5^2)+....` equals a.`pi^2//8` b. `pi^2//12` c. `pi^2//3` d. `pi^2//2`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    CENGAGE ENGLISH|Exercise All Questions|9 Videos
  • STRAIGHT LINES

    CENGAGE ENGLISH|Exercise All Questions|491 Videos

Similar Questions

Explore conceptually related problems

If 1/(1^2)+1/(2^2)+1/(3^2)+ tooo=(pi^2)/6,t h e n1/(1^2)+1/(3^2)+1/(5^2)+ equals pi^2//8 b. pi^2//12 c. pi^2//3 d. pi^2//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)(-sqrt(3)//2)\ is- a. -pi//3 b. -2pi//3 c. 4pi//3 d. 5pi//3

int_0^(pi//2)xsinx\ dx is equal to a. pi//2 b. pi//4 c. pi d. 1

If int_0^a1/(1+4x^2)dx=\ pi/8 , then a equals a. pi/2 b. pi/4 c. 1/2 d. 1

The argument of (1-i)/(1+i) is a. -pi/2 b. pi/2 c. (3pi)/2 d. (5pi)/2

(lim)_(xvecpi/2)((1-sin x)(8x^3-pi^3)cos x)/((pi-2x)^4) a. (pi^2)/6 b. (3pi^2)/(16) c. (pi^2)/(16) d. -(3pi^2)/(16)

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)

int_0^(pi//2)1/(1+cot^3x)dx is equal to a 0 b. 1 c. pi//2 d. pi//4

sin^2 pi/6 +cos^2 pi/3 -tan^2 pi/4=-1/2

CENGAGE ENGLISH-SEQUENCES AND SERIES-All Questions
  1. If the terms of the A.P, sqrt(a-x),sqrt(x),sqrt(a+x) are all in integ...

    Text Solution

    |

  2. For a ,x ,>0 prove tht at most one term of the G.P. sqrt(a-x),sqrt(x),...

    Text Solution

    |

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

    Text Solution

    |

  4. Coefficient of x^(18) in (1+x+2x^2+3x^3++18 x^(18))^2 equal to 995 b. ...

    Text Solution

    |

  5. Let alphaa n dbeta be the roots of x^2-x+p=0a n dgammaa n ddelta be th...

    Text Solution

    |

  6. If the sum of the first 2n terms of the A.P. 2, 5, 8, ..., is equal to...

    Text Solution

    |

  7. Statement 1: If the arithmetic mean of two numbers is 5/2 geometric ...

    Text Solution

    |

  8. Let the positive numbers a ,b ,ca d nd be in the A.P. Then a b c ,a b ...

    Text Solution

    |

  9. If three positive real numbers a,b ,c are in A.P such that a b c=4 , t...

    Text Solution

    |

  10. Consider an infinite geometric series with first term a and common rat...

    Text Solution

    |

  11. The maximum sum of the series 20+19 1/3+18 2/3+...... is (A) 310 (...

    Text Solution

    |

  12. In the quadratic equation ax^2+bx+c=0,Delta = b^2-4ac and alpha+beta,a...

    Text Solution

    |

  13. Let a1,a2,a3,... be in harmonic progression with a1=5a n da(20)=25. ...

    Text Solution

    |

  14. An infinite G.P. has first term as a and sum 5, then a belongs to a) |...

    Text Solution

    |

  15. Let Ssub(0,pi) denote the set of values of x satisfying the equation 8...

    Text Solution

    |

  16. The value of sum(r=0)^n(a+r+a r)(-a)^r is equal to a.(-1)^n[(n+1)a^(n+...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  19. If bi=1-ai ,n a=sum(i=1)^n ai ,n b=sum(i=1)^n bi ,t h e nsum(i=1)^n ai...

    Text Solution

    |

  20. The greatest integer by which 1+sum(r=1)^(30)rxxr ! is divisible is a....

    Text Solution

    |