Home
Class 12
MATHS
Find the sequence of the numbers defined...

Find the sequence of the numbers defined by
`a_(n)={{:(1/n,"when n is odd"),(-1/n,"when n is even"):}`

Text Solution

Verified by Experts

Using `a_(n)=1/n,` we have
`a_(1)=1,a_(3)=1/3,a_(5)=1/5`,…
Using `a_(n)=-1/n`, we have
`a_(2)=-1/2,a_(4)=-1/4,a_(6)=-1/6,…`
Promotional Banner

Topper's Solved these Questions

  • PROGRESSION AND SERIES

    CENGAGE|Exercise Exercise 5.1|3 Videos

  • PROGRESSION AND SERIES

    CENGAGE|Exercise Exercise 5.2|10 Videos

  • PROGRESSION AND SERIES

    CENGAGE|Exercise Single correct Answer|54 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

Find the sequence of the numbers defined by- when n is odd-,when n is even

A function f from the set of natural number to integers defined by f(n)={{:(,(n-1)/(2),"when n is odd"),(,-(n)/(2),"when n is even"):}

a. Find the 21 st and 42 nd terms of the sequence defined by: t_(n)={(0,"if n is odd"),(1,"if n is even"):} (b) Find the 18 th and 25 th terms of the sequence defined by t_(n)={(n(n+2),"if n is even natural number"),((4n)/(n^(2)+1),"ifn is odd natural number"):} (c) Find the 440th and 441st terms of the sequance given by: t_(n)={(n/(n/44-1),"If n is not the square ofa natural nunber"),(2.7,"if n is the square of a natural number"):}

Show that the function f:N rarr Z, defined by f(n)=(1)/(2)(n-1) when n is odd ;-1/2 n when n is even is both one-one and onto

Find the first five terms of the sequence whose general term is given by a_(n)={ {:(n^(2) -1,",if n is odd"),((n^(2) +1)/(2),",if n is even "):}

Find the sum of n terms of the sequence (a_(n)), where a_(n)=5-6n,n in N

find first 5 terms of the sequences, defined by a_(1) =-1 , a_(n) = ( a_(n-1))/n " for n ge 2

Write the first five terms of the sequence defined by a_(n)=(-1)^(n-1).2^(n)

CENGAGE-PROGRESSION AND SERIES-Examples
  1. Write down the sequence whose nth term is 2^n//n and (ii) [3+(-1)^n]/...

    Text Solution

    |

  2. Find the sequence of the numbers defined by a(n)={{:(1/n,"when n is ...

    Text Solution

    |

  3. Write the first three terms of the sequence defined by a1 2,a(n+1)=(2a...

    Text Solution

    |

  4. The Fobonacci sequence is defined by 1=a1=a2a n dan=a(n-1)+a(n-2,)n > ...

    Text Solution

    |

  5. A sequence of integers a1+a2++an satisfies a(n+2)=a(n+1)-anforngeq1 . ...

    Text Solution

    |

  6. Show that the sequence 9,12,15,18,... is an A.P. Find its 16th term...

    Text Solution

    |

  7. Show that the sequence loga ,log(a b),log(a b^2),log(a b^3), is an A.P...

    Text Solution

    |

  8. In a certain A.P., 5 times the 5th term is equal to 8 times the 8th te...

    Text Solution

    |

  9. Find the term of the series 25 ,22 ,3/4,20 1/2,18 1/4 which is numeric...

    Text Solution

    |

  10. If pth, qth and rth terms of an A.P. are a,b,c, respectively, then sho...

    Text Solution

    |

  11. Consider two A.P. s: S1:2,7,12 ,17 , 500t e r m s a n dS1:1,8,15 ,22 ,...

    Text Solution

    |

  12. If a1,a2,a3, ,an are in A.P., where ai >0 for all i , show that 1/(sqr...

    Text Solution

    |

  13. If p,q and r (pneq) are terms ( not necessarily consecutive) of an A.P...

    Text Solution

    |

  14. If the terms of the A.P. sqrt(a-x),sqrt(x),sqrt(a+x) are all in intege...

    Text Solution

    |

  15. If (b+c-a)/a,(c+a-b)/b,(a+b-c)/c are in A.P. Prove that 1/a,1/b,1/c ar...

    Text Solution

    |

  16. If a ,b ,c in R+ form an A.P., then prove that a+1//(b c),b+1//(1//a ...

    Text Solution

    |

  17. If a,b,c are in A.P., then prove that the following are also in A.P ...

    Text Solution

    |

  18. If the sum of three numbers in A.P., is 24 and their product is 440...

    Text Solution

    |

  19. Divide 32 into four parts which are in A.P. such that the ratio of the...

    Text Solution

    |

  20. The digits of a positive integer, having three digits, are in A.P. and...

    Text Solution

    |