Home
Class 11
MATHS
Let a+a r1+a r1 2++ooa n da+a r2+a r2 2+...

Let `a+a r_1+a r1 2++ooa n da+a r_2+a r2 2++oo` be two infinite series of positive numbers with the same first term. The sum of the first series is `r_1` and the sum of the second series `r_2dot` Then the value of `(r_1+r_2)` is ________.

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

Find the sum of the series sum_(r=1)^n rxxr !dot

If the sum to the infinity of the series 3+5r+7r^2+.... is 44/9 then find the value of r

Write the sum of n term fo a series whose r^(t h) term is: r+2^rdot

The sum of the series sum_(r=0) ^(n) ""^(2n)C_(r), is

Sum of the series sum_(r=1)^(n) (r^(2)+1)r! is

If the r^(th) term of a series is 1 + x + x^2 + .......+ x^(r-1) , then the sum of the first n terms is

Find the sum of firs 100 terms of the series whose general term is given by T_(r)=(r^(2)+1)r! .

The sum of the series sum_(r=0) ^(n) "r."^(2n)C_(r), is

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

Write down the series whose r^(th) term is 3. 2 ^(r + 1 ) . Is it a geometric series ?

CENGAGE ENGLISH-SEQUENCES AND SERIES-All Questions
  1. If a1, a2, a3, an are in H.P. and f(k)=(sum(r=1)^n ar)-ak ,t h e n (a...

    Text Solution

    |

  2. If a ,b ,c are in A.P., the a/(b c),1/c ,1/b will be in a. A.P b. G.P....

    Text Solution

    |

  3. Let a+a r1+a r1 2++ooa n da+a r2+a r2 2++oo be two infinite series of ...

    Text Solution

    |

  4. The coefficient of the quadratic equation a x^2+(a+d)x+(a+2d)=0 are co...

    Text Solution

    |

  5. Let S denote sum of the series 3/(2^3)+4/(2^4 .3)+5/(2^6 .3)+6/(2^7 .5...

    Text Solution

    |

  6. Let the sum of first three terms of G.P. with real terms be 13/12 and ...

    Text Solution

    |

  7. Given a,b,c are in A.P.,b,c,d are in G.P and c,d,e are in H.P .If a=2 ...

    Text Solution

    |

  8. The terms a1,a2,a3 form an arithmetic sequence whose sum is 18.The ter...

    Text Solution

    |

  9. Let f(x)=2x+1. Then the number of real number of real values of x for ...

    Text Solution

    |

  10. Concentric circles of radii 1,2,3,. . . . ,100 c m are drawn. The inte...

    Text Solution

    |

  11. Let {tn} be a sequence of integers in G.P. in which t4: t6=1:4 and t2+...

    Text Solution

    |

  12. If x ,2y ,3z are in A.P., where the distinct numbers x ,y ,z are in G....

    Text Solution

    |

  13. If Sp denotes the sum of the series 1+r^p+r^(2p)+ toooa n dsp the sum ...

    Text Solution

    |

  14. If x ,y ,z are real and 4x^2+9y^2+16 z^2-6x y-12 y z-8z x=0,t h e nx ,...

    Text Solution

    |

  15. If a1, a2, ,an are in H.P., then (a1)/(a2+a3++an),(a2)/(a1+a3++an), ...

    Text Solution

    |

  16. If H1, H2, ,H(20) are 20 harmonic means between 2 and 3, then (H1+2)/...

    Text Solution

    |

  17. A pack contains n cards numbered from 1 to n. Two consecutive numbered...

    Text Solution

    |

  18. Let an=16 ,4,1, be a geometric sequence. Define Pn as the product o...

    Text Solution

    |

  19. If he equation x^3+a x^2+b x+216=0 has three real roots in G.P., then ...

    Text Solution

    |

  20. Let Tr be the rth term of an A.P., for r=1,2,3,..... If for some pos...

    Text Solution

    |