Home
Class 12
MATHS
If t(1)=1,t(r )-t( r-1)=2^(r-1),r ge 2, ...

If `t_(1)=1,t_(r )-t_( r-1)=2^(r-1),r ge 2`, find `sum_(r=1)^(n)t_(r )`.

Text Solution

AI Generated Solution

To solve the problem, we need to find the sum \( S_n = \sum_{r=1}^{n} t_r \) given the recurrence relation \( t_r - t_{r-1} = 2^{r-1} \) for \( r \geq 2 \) and \( t_1 = 1 \). ### Step-by-Step Solution: 1. **Identify the first term**: \[ t_1 = 1 \] ...
Promotional Banner

Topper's Solved these Questions

  • SEQUENCES AND SERIES

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|38 Videos

  • SEQUENCES AND SERIES

    ARIHANT MATHS ENGLISH|Exercise Exercise (Statement I And Ii Type Questions)|7 Videos

  • PROPERTIES AND SOLUTION OF TRIANGLES

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|21 Videos

  • SETS, RELATIONS AND FUNCTIONS

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|12 Videos

Similar Questions

Explore conceptually related problems

If T_r=r(r^2-1), then find sum_(r=2)^oo1/Tdot

If sum_(r=1)^n t_r=n/8(n+1)(n+2)(n+3), then find sum_(r=1)^n1/(t_r)dot

If Sigma_(r=1)^(n) T_(r)=n(2n^(2)+9n+13) , then find the sum Sigma_(r=1)^(n)sqrt(T_(r)) .

If sum_(r=1)^n T_r=(3^n-1), then find the sum of sum_(r=1)^n1/(T_r) .

Let t_r=2^(r/2)+2^(-r/2) then sum_(r=1)^10 t_r^2=

Find the sum sum_(r=1)^n r/(r+1)!

Let T_(r) be the r^(th) term of a sequence, for r=1,2,3,......... If 3T_(r+1)=T_(r) and T_(7)=(1)/(243) then the value of sum_(r=1)^(oo)(T_(r).T_(r+1)) is :

If sum_(r=1)^n T_r=n(2n^2+9n+13), then find the sum sum_(r=1)^nsqrt(T_r)dot

If D_(r) = |(r,1,(n(n +1))/(2)),(2r -1,4,n^(2)),(2^(r -1),5,2^(n) -1)| , then the value of sum_(r=1)^(n) D_(r) , is

If sum _(r =1) ^(n ) T _(r) = (n +1) ( n +2) ( n +3) then find sum _( r =1) ^(n) (1)/(T _(r))

ARIHANT MATHS ENGLISH-SEQUENCES AND SERIES-Exercise (Subjective Type Questions)
  1. If the first four terms of an arithmetic sequence are a,2a,b and (a-6-...

    Text Solution

    |

  2. If 1/1^2+1/2^2+1/3^2+...oo=pi^2/6 then value of 1-1/2^2+1/3^2-1/4^2+.....

    Text Solution

    |

  3. If the arithmetic mean of a(1),a(2),a(3),"........"a(n) is a and b(1),...

    Text Solution

    |

  4. If a(1),a(2),a(3),"........" is an arithmetic progression with common ...

    Text Solution

    |

  5. If t(1)=1,t(r )-t( r-1)=2^(r-1),r ge 2, find sum(r=1)^(n)t(r ).

    Text Solution

    |

  6. Prove that I(1),I(2),I(3)"..." form an AP, if I(n)=int(0)^(pi)(sin...

    Text Solution

    |

  7. Consider the sequence S=7+13+21+31+".....+"T(n) , find the value of T(...

    Text Solution

    |

  8. Find value of (x+(1)/(x))^(3)+(x^(2)+(1)/(x^(2)))^(3)+"........"+(x^(n...

    Text Solution

    |

  9. If the sequence a1, a2, a3,....... an ,dot forms an A.P., then prove ...

    Text Solution

    |

  10. If three unequel numbers are in HP and their squares are in AP, show ...

    Text Solution

    |

  11. Ifa(1),a(2),a(3),"........",a(n) are in AP with a(1)=0, prove that (a(...

    Text Solution

    |

  12. Balls are arranged in rows to form an equilateral triangle. The first ...

    Text Solution

    |

  13. If theta(1),theta(2),theta(2), theta(3),"…………" Theta(n) are in AP w...

    Text Solution

    |

  14. Show that,(1+5^(-1))(1+5^(-2))(1+5^(-4))(1+5^(-8))"....."(1+5^(-2n))= ...

    Text Solution

    |

  15. Evaluate S=sum(n=0)^n(2^n)/((a^(2^n)+1) (where a>1).

    Text Solution

    |

  16. Find the sum of the series :tan^- 1(1/3)+tan^- 1(2/9)+....+tan^- 1((2^...

    Text Solution

    |

  17. Find the sum to n terms, whose nth term is tan[alpha+(n-1)beta]tan (al...

    Text Solution

    |

  18. If sum(r=1)^n tr=n/8(n+1)(n+2)(n+3), then find sum(r=1)^n1/(tr)dot

    Text Solution

    |

  19. If s1,s2,s3 denote the sum of n terms of 3 arithmetic series whose fir...

    Text Solution

    |

  20. Three friends whose ages form a G.P. divide a certain sum of money in ...

    Text Solution

    |