Home
Class 11
MATHS
If 1+(1+2)/2+(1+2+3)/3+ddotto\ n terms i...

If `1+(1+2)/2+(1+2+3)/3+ddotto\ n` terms is `Sdot` Then, `S` is equal to `(n(n+3))/4` b. `(n(n+2))/4` c. `(n(n+1)(n+2))/6` d. `n^2`

A

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

B

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

C

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

D

`n^(2)`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • SEQUENCES AND SERIES

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|129 Videos
  • QUADRATIC EXPRESSIONS AND EQUATIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|50 Videos
  • SETS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|30 Videos

Similar Questions

Explore conceptually related problems

If 1+(1+2)/2+(1+2+3)/3+ddotto\ n terms is Sdot Then, S is equal to a. (n(n+3))/4 b. (n(n+2))/4 c. (n(n+1)(n+2))/6 d. n^2

The total number of ways of selecting two numbers from the set {1,2, 3, 4, ........3n} so that their sum is divisible by 3 is equal to a. (2n^2-n)/2 b. (3n^2-n)/2 c. 2n^2-n d. 3n^2-n

The sum of the series 1+4+3+6+5+8+ upto n term when n is an even number (n^2+n)/4 2. (n^2+3n)/2 3. (n^2+1)/4 4. (n(n-1))/4 (n^2+3n)/4

S_n=3/(1^2)+5/(1^2+2^2)+7/(1^2+2^2+3^2)+ upto n terms, then a. S_n=(6n)/(n+1) b. S_n=(6(n+2))/(n+1) c. S_oo=6 d. S_oo=1

If the sum of first n terms of an A P is c n^2, then the sum of squares of these n terms is (2009) (n(4n^2-1)c^2)/6 (b) (n(4n^2+1)c^2)/3 (n(4n^2-1)c^2)/3 (d) (n(4n^2+1)c^2)/6

If f(r)=1+1/2+1/3+1/ra n df(0)=0,t h e nsum_(r=1)^n(2r+1)f(r) is equal to (a) nf(n+1)-((n^2-3n+2))/2 (b) (n+1)^2f(n)-((n^2-3n+2))/2 (c) (n+1)^2f(n+1)-((n^2+3n+2))/2 (d) (n+1)^f(n+1)-((n^2-3n+2))/2

Let f(n)=1+1/2+1/3++1/ndot Then f(1)+f(2)+f(3)++f(n) is equal to (a) nf(n)-1 (b) (n+1)f(n)-n (c) (n+1)f(n)+n (d) nf(n)+n

If n is a non zero rational number then show that 1 + n/2 + (n (n - 1))/(2.4) + (n(n-1)(n - 2))/(2.4.6) + ….. = 1 + n/3 + (n (n + 1))/(3.6) + (n (n + 1) (n + 2))/(3.6.9) + ….

If a 1 , a 2 , a 3 , , a 2 n + 1 are in A.P., then a 2 n + 1 − a 1 a 2 n + 1 + a 1 + a 2 n − a 2 a 2 n + a 2 + + a n + 2 − a n a n + 2 + a n is equal to a. n ( n + 1 ) 2 × a 2 − a 1 a n + 1 b. n ( n + 1 ) 2 c. ( n + 1 ) ( a 2 − a 1 ) d. none of these

If the sum of n term of the series (5)/(1.2.3) + (6)/(2.3.4) + ( 7)/(3.4.5)+"…." is a/2 - (n+b)/((n+1)(n+2)) , then

OBJECTIVE RD SHARMA ENGLISH-SEQUENCES AND SERIES-Chapter Test
  1. Natural numbers are written as 1, (2,3), (4,5,6).. Show that the sum...

    Text Solution

    |

  2. If the first term of an A.P. is 2 and common difference is 4, then ...

    Text Solution

    |

  3. If 1+(1+2)/2+(1+2+3)/3+ddotto\ n terms is Sdot Then, S is equal to (n(...

    Text Solution

    |

  4. The sum of 10 terms of the series sqrt(2)+sqrt(6)+sqrt(18)+ddoti s\ ...

    Text Solution

    |

  5. The (m+n)th and (m-n)th terms of a GP are p and q, respectively. Then,...

    Text Solution

    |

  6. The fourth, seventh and tenth terms of a G.P. are p,q,r respectively, ...

    Text Solution

    |

  7. The sum of the integers from 1 to 100 which are not divisible by 3 or ...

    Text Solution

    |

  8. Let the harmonic mean and geometric mean of two positive numbers be in...

    Text Solution

    |

  9. The sum of the series 1 + 2.2+ 3.2^(2) + 4.2^(3) + 5.2^(4) + ….. +...

    Text Solution

    |

  10. If a\ (1/b+1/c),\ b(1/c+1/a),\ c(1/a+1/b) are in A.P. prove that a ,\ ...

    Text Solution

    |

  11. If the m^(th),n^(th)andp^(th) terms of an A.P. and G.P. be equal and b...

    Text Solution

    |

  12. The 7th term of a H.P. is (1)/(10) and 12 th term is (1)/(25), find th...

    Text Solution

    |

  13. The length of side of a square is 'a' metre. A second square is formed...

    Text Solution

    |

  14. The harmonic mean of the roots of the equation (5+sqrt(2))x^2-(4+sqrt(...

    Text Solution

    |

  15. If three positive real numbers a,b,c, (cgta) are in H.P., then log(a+c...

    Text Solution

    |

  16. In an A.P., the p^(th) term is 1/q and the q^(th) term is 1/p. fin...

    Text Solution

    |

  17. The sum of the series 2/3+8/9+(26)/(27)+(80)/(81)+ to n terms is (a) n...

    Text Solution

    |

  18. If a,b,c are in H.P. , then

    Text Solution

    |

  19. The odd value of n for which 704+1/2(704)+… upto n terms = 1984-1/2(1...

    Text Solution

    |

  20. The positive interger n for which 2xx2^2+3xx 2^3+4xx2^4+….+nxx2^4=2^(n...

    Text Solution

    |