Home
Class 12
MATHS
If S(n)=(1.2)/(3!)+(2.2^(2))/(4!)+(3.2^(...

If `S_(n)=(1.2)/(3!)+(2.2^(2))/(4!)+(3.2^(2))/(5!)+...+` up to `n` terms, then sum of infinite terms is

A

`(4)/(pi)`

B

`(3)/(e)`

C

`(pi)/(r )`

D

`1`

Text Solution

Verified by Experts

The correct Answer is:
D
`(d)` Here `t_(r )=(r*2^(r ))/((r+2)!)=((r+2-2)2^(r ))/((r+2)!)=(2^(r ))/((r+1)!)-(2^(r+1))/((r+2)!)`
`:.S_(n)=sum_(r=1)^(n)t_(r )=sum_(r=1)^(n)(2^(r ))/((r+1)!)-(2^(r+1))/((r+2)!)=1-(2^(n+1))/((n+2)!)`
`:.S_(oo)=lim_(ntooo)(1-(2^(n+1))/((n+2)!))=1`
Promotional Banner

Topper's Solved these Questions

  • PROGRESSION AND SERIES

    CENGAGE|Exercise Examples|120 Videos

  • PROGRESSION AND SERIES

    CENGAGE|Exercise Exercise 5.1|3 Videos

  • PROGRESSION AND SERIES

    CENGAGE|Exercise Multiple Correct Answer|4 Videos

  • PROBABILITY II

    CENGAGE|Exercise NUMARICAL VALUE TYPE|2 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE|Exercise JEE Advanced Previous Year|11 Videos

Similar Questions

Explore conceptually related problems

If S_(n)=(1.2)/(3!)+(2.2^(2))/(4!)+(3.2^(3))/(5!)+... upto n terms then the sum infinite terms is

The sum of 1+(2)/(5)+(3)/(5^(2))+(4)/(5^(3))+.... upto n terms

(1)/(2)+(3)/(4)+(5)/(8) The sum of the series infinite terms is

The sum of series (1)/(2)+(3)/(2^(2))+(5)/(2^(3))+(7)/(2^(4))+... up to infinite terms is equal to

Sum of the following series 1+(2)/(2)+(3)/(2^(2))+(4)/(2^(3))+... to n terms

The sum of the series (1+2)+(1+2+2^(2))+(1+2+2^(2)+2^(3))+ . . . up to n terms, is

If S_(1), S_(2), S_(3),….., S_(n) are the sum of infinite geometric series whose first terms are 1,3,5…., (2n-1) and whose common rations are 2/3, 2/5,…., (2)/(2n +1) respectively, then {(1)/(S_(1) S_(2)S_(3))+ (1)/(S_(2) S_(3) S_(4))+ (1)/(S_(3) S_(4)S_(5))+ ........."upon infinite terms"}=

CENGAGE-PROGRESSION AND SERIES-Single correct Answer
  1. The sum of n terms of series ab+(a+1)(b+1)+(a+2)(b+2)+…+(a+(n-1)(b+(n-...

    Text Solution

    |

  2. sum(i=1)^(oo)sum(j=1)^(oo)sum(k=1)^(oo)(1)/(a^(i+j+k)) is equal to (wh...

    Text Solution

    |

  3. The coefficient of x^(1274) in the expansion of (x+1)(x-2)^(2)(x+3)^(3...

    Text Solution

    |

  4. If the positive integers are written in a triangular array as shown be...

    Text Solution

    |

  5. The value of sum(i=1)^(n)sum(j=1)^(i)sum(k=1)^(j)=220 , then the value...

    Text Solution

    |

  6. The sum sum(k=1)^(10)underset(i ne j ne k)underset(j=1)(sum^(10))sum(i...

    Text Solution

    |

  7. The sum sum(k=1)^(10)underset(i lt j lt k)underset(j=1)(sum^(10))sum(i...

    Text Solution

    |

  8. If the sum to infinty of the series , 1+4x+7x^(2)+10x^(3)+…., is (35)/...

    Text Solution

    |

  9. The value of sum(n=1)^oo(-1)^(n+1)(n/(5^n)) equals

    Text Solution

    |

  10. Find the sum of the infinte series (1)/(9)+(1)/(18)+(1)/(30)+(1)/(45)+...

    Text Solution

    |

  11. If sum(r=1)^(r=n)(r^(4)+r^(2)+1)/(r^(4)+r)=(675)/(26), then n equal to

    Text Solution

    |

  12. The sequence {x(k)} is defined by x(k+1)=x(k)^(2)+x(k) and x(1)=(1)/(2...

    Text Solution

    |

  13. The absolute value of the sum of first 20 terms of series, if S(n)=(n+...

    Text Solution

    |

  14. If S(n)=(1^(2)-1+1)(1!)+(2^(2)-2+1)(2!)+...+(n^(2)-n+1)(n!), then S(50...

    Text Solution

    |

  15. If S(n)=(1.2)/(3!)+(2.2^(2))/(4!)+(3.2^(2))/(5!)+...+ up to n terms, t...

    Text Solution

    |

  16. There is a certain sequence of positive real numbers. Beginning from t...

    Text Solution

    |

  17. The sequence {x(1),x(2),…x(50)} has the property that for each k, x(k)...

    Text Solution

    |

  18. Let a(0)=0 and a(n)=3a(n-1)+1 for n ge 1. Then the remainder obtained ...

    Text Solution

    |

  19. Suppose a(1),a(2),a(3),….,a(2012) are integers arranged on a cicle. Ea...

    Text Solution

    |

  20. The sum of the series (9)/(5^(2)*2*1)+(13)/(5^(3)*3*2)+(17)/(5^(4)*4*3...

    Text Solution

    |