Home
Class 11
MATHS
Let a1,a2 ,a3 ...... be an A.P. Prove th...

Let `a_1,a_2 ,a_3` ...... be an A.P. Prove that `sum_(n=1)^(2m)(-1)^(n-1)a_n^2=m/(2m-1)(a_1^2-a_(2m)^2)`.

Promotional Banner

Topper's Solved these Questions

  • PROBABILITY

    PATHFINDER|Exercise QUESTION BANK|41 Videos

  • QUADRATIC EQUATION

    PATHFINDER|Exercise QUESTION BANK|19 Videos

Similar Questions

Explore conceptually related problems

Prove that: sum_(m=1)^ntan^(-1)((2m)/(m^4+m^2+2))=tan^(-1)((n^2+n)/(n^2+n+2))

If the sequence a_1, a_2, a_3,....... a_n ,dot forms an A.P., then prove that a_1^2-a_2^2+a_3^2-a_4^2+.......+ a_(2n-1)^2 - a_(2n)^2=n/(2n-1)(a_1^2-a_(2n)^2)

If a_1, a_2,...... ,a_n >0, then prove that (a_1)/(a_2)+(a_2)/(a_3)+(a_3)/(a_4)+.....+(a_(n-1))/(a_n)+(a_n)/(a_1)> n

If a_1,a_2,a3,...,a_n are in A.P then show that 1/(a_1a_2)+1/(a_2a_3)+1/(a_3a_4)+...+1/(a_(n-1)a_n)=(n-1)/(a_1a_n)

Find the sum of first 24 terms of the A.P. a_1,a_2, a_3 ......., if it is inown that a_1+a_5+a_(10)+a_(15)+a_(20)+a_(24)=225.

If a_1,a_2,a_3...a_n are in HP and f(k)=sum_(r=1)^na_r-a_k, then a_1/(f(1)),a_2/(f(2)),a_3/(f(3)),......a_n/(f(n)) are in

Let a_1 , a_2 , a_3,.... be terms of an A.P. if (a_1 + a_2 +....+ a_p)/(a_1 + a_2 +...+ a_q) = p^2/q^2. p ne q then a_6/a_21 equals

If a_1, a_2,a_3, ,a_n is an A.P. with common difference d , then prove that "tan"[tan^(-1)(d/(1+a_1a_2))+tan^(-1)(d/(1+a_2a_3))+......+tan^(-1)(d/(1+a_(n-1)a_n))]=((n-1)d)/(1+a_1a_n)

Let a_1,a_2,a_3,.......a_11 be real number satisfying a_1=15,27-2a_2gt0 anda_k=2a_(k-1)-a_(k-2) for k=3,4,.....11. If (a_1^2+a_2^2+......a_11^2)/11=90, then the value of (a_1 +a_2+.....a_11)/11 is equal to

If the coefficients of four consecutive terms in the expansion of (1+x)^n are a_1,a_2,a_3 and a_4 respectively. then prove that a_1/(a_1+a_2)+a_3/(a_3+a_4)=2a_2/(a_2+a_3).

PATHFINDER-PROGRESSION AND SERIES -QUESTION BANK
  1. Let Sn denote the sum upto n terms of an AP . If Sn=n^2P and Sm=m^2P ...

    Text Solution

    |

  2. If s1 ,s2 and s3 are the sum of first n,2n,3n terms respectively of an...

    Text Solution

    |

  3. Let a1,a2 ,a3 ...... be an A.P. Prove that sum(n=1)^(2m)(-1)^(n-1)an^2...

    Text Solution

    |

  4. A G.P. consists of 2n terms . If the sum of the terms occupying the od...

    Text Solution

    |

  5. If G1 ,G2 are geometric means , and A is the arithmetic mean between ...

    Text Solution

    |

  6. Show that abs((a,b,aalpha+b),(b,c,balpha+c),(aalpha+b,balpha+c,0):}=0 ...

    Text Solution

    |

  7. If Sn=1+1/2+1/2^2+........+1/2^(n-1) . Calculate the least value of n ...

    Text Solution

    |

  8. Prove that the number of the sequence 121,12321,1234321,...... are eac...

    Text Solution

    |

  9. Find the sum of n terms of series 1+5((4n+1)/(4n-3))+9((4n+1)/(4n-3))^...

    Text Solution

    |

  10. Find the sum of the products of the integers 1,2,3,....n taken two at ...

    Text Solution

    |

  11. Sum the series n+(n-1)x+(n-2)x^2+.......+2x^(n-2)+x^(n-1).

    Text Solution

    |

  12. Find 1+2^2x+3^2x^2+4^2x^3+.... to infty absx lt 1.

    Text Solution

    |

  13. Find the sum of 1st n terms of the sequence 3,6,15,42,123,...

    Text Solution

    |

  14. Let Sn denote the sum of first n terms of the sequence 1,5,14,30,55,.....

    Text Solution

    |

  15. Finds the sum of first n terms of the series 3/(1^2xx2^2)+5/(2^2xx3^2)...

    Text Solution

    |

  16. How many terms of the series 54+51+48+45+ ... must be taken to make 51...

    Text Solution

    |

  17. If (b+c),(c+a),(a+b) are in H.P. show that a^2 ,b^2 , c^2 are in A.P.

    Text Solution

    |

  18. Find the sum of first n terms of the series 3/1^2+5/(1^2+2^2)+7/(1^2+2...

    Text Solution

    |

  19. If 0 < theta < pi/2 then find the least value of tantheta+cottheta

    Text Solution

    |

  20. If x and y are positive quantities whose sum is 4, show that (x+1/x)^2...

    Text Solution

    |