Home
Class 12
MATHS
The value of the sum 1.2.3+2.3.4+3.4.5...

The value of the sum 1.2.3+2.3.4+3.4.5+… upto n terms is equal to

A

`(1)/(6)n^(2)(2n^(2)+1)`

B

`(1)/(6)(n^(2)-1)(2n-1)(2n+3)`

C

`(1)/(8)(n^(2)+1)(n^(2)+5)`

D

`(1)/(4)n(n+1)(n+2)(n+3)`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • EAMCET-2019 (TS) SHIFT-1

    SIA PUBLICATION|Exercise CHEMISTRY|10 Videos

  • HYPERBOLIC FUNCTIONS

    SIA PUBLICATION|Exercise Problems|16 Videos

Similar Questions

Explore conceptually related problems

2+ 4+ 7 + 11 + 16 + ….. upto n terms is equal to

The value of 2/3 + 3/4 + 1/2 is

2+ 3.2 + 4.2^(2) + …... upto n terms =

Using the principle of finite Mathematical Induction prove that 1.2.3+2.3.4+3.4.5.+………… upto n terms = n(n+1)(n+2)(n+3))/4,for all n in N

The sum of the sequence 5+55+555+… upto n terms is

The Value of 1 3/5+4 2/7=

2.4 + 4.7 + 6.10+ …. upto (n-1) terms=

1^(2) + 3^(2) + 5^(2) + …. upto n terms =

Using the principle of finite Mathematical Indcution prove that 2.3 + 3.4 + 4.5 + ……."upto n terms" = (n(n^(2)+6n+11))/(3) .

SIA PUBLICATION-FUNCTIONS AND MATHEMATICAL INDUCTION -Problems
  1. If f:R rarr R, g:R rarr R are defined by f(x)= 5x-3,g(x)=x^(2)+3, then...

    Text Solution

    |

  2. If A={x inR//(pi)/(4)lexle(pi)/(3)} and f(x)=sinx-x, then f(A) is equa...

    Text Solution

    |

  3. The value of the sum 1.2.3+2.3.4+3.4.5+… upto n terms is equal to

    Text Solution

    |

  4. If x=(1)/(5)+(1.3)/(5.10)+(1.3.5)/(5.10.15)+….oo then find 3x^(2)+6x.

    Text Solution

    |

  5. If R is the set of all real numbers and f : R - {2}to R is defined by ...

    Text Solution

    |

  6. Let Q be the set of all rational number in [0, 1] and f:[0, 1]rarr[0, ...

    Text Solution

    |

  7. sum(k=1)^(2n+1)(-1)^(k-1)k^(2) equals to

    Text Solution

    |

  8. If f(x)=(p-x^(n))^(1//n), p gt 0 and n is a positive integer, then f[f...

    Text Solution

    |

  9. The value of {x in R[log(1.6)^(1-x^(2))-(0.625)^(6(1+8))]in R}

    Text Solution

    |

  10. If f : R to R^(2) and R^(+)to R are such that g{f(x)}=|sin x| and f{(g...

    Text Solution

    |

  11. Define f:Z rarrZ by f(x)={{:(x//2,"(x is even)"),(0,"(x is odd)"):} th...

    Text Solution

    |

  12. If (1)/(2xx4)+(1)/(4xx6)+(1)/(6xx8)+…. (n terms) =(kn)/(n+1), then k i...

    Text Solution

    |

  13. If f:[2, oo)rarrB defined by f(x)=x^(2)-4x+5 is a bijection, then B=

    Text Solution

    |

  14. If f : R to R is defined by f(x)=[(x)/(5)] for x in R, where [y] denot...

    Text Solution

    |

  15. If a,b and n are natural numbers, then a^(2n-1)+b^(2a-1) is divisible ...

    Text Solution

    |

  16. If f(0)=0, f(1)=1, f(2)=2 and f(x)=f(x-2)+f(x-3) " for " x=3, 4, 5, ……...

    Text Solution

    |

  17. Let R denote the set of all real numbers and R^(+) denote the set of a...

    Text Solution

    |

  18. The numbers a(n)=6^(n)-5n for n=1,2,3,… whrn divided by 25 leave the r...

    Text Solution

    |

  19. If f:[2, 3] rarr RR is defined by f(x)=x^(3)+3x-2, then the range f(x)...

    Text Solution

    |

  20. {x in RR:(2x-1)/(x^(3)+4x^(2)+3x) in RR}=

    Text Solution

    |