Home
Class 12
MATHS
Find the sum of the products of the ten ...

Find the sum of the products of the ten numbers `+-1,+-2,+-3,+-4,a n d+-5` taking two at a time.

Text Solution

Verified by Experts

We have,
`(1-1+2-2+..+5-5)^(2)`
`=1^(2)+1^(2)+2^(2)+2^(2)+…+5^(2)+5^(2)+2S`,
where S is the required sum. Hence,
`0=2(1^(2)+2^(2)+3^(2)+4^(2)+5^(2))+2S`
or S=-55
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 Multiple Correct Answer|4 Videos

  • PROBABILITY II

    CENGAGE|Exercise JEE Advanced Previous Year|25 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE|Exercise JEE Advanced Previous Year|11 Videos

Similar Questions

Explore conceptually related problems

There are two sets A and B each of which consists of three numbers in A.P.whose sum is 15 and where D and d are the common differences such that D-d=1. If p/q=7/8 , where p and q are the product of the numbers ,respectively, and d gt 0 in the two sets . The sum of the products of the numbers is set A taken two at at time is

Find the sum of all the numbers that can be formed with the digits 2, 3, 4, 5 taken all at a time.

If the product of n positive numbers is n^n . Then their sum is

Consider the ten numbers a r ,a r^2, a r^3, ,a r^(10)dot If their sum is 18 and the sum of their reciprocals is 6, then the product of these ten numbers is 81 b. 243 c. 343 d. 324

Find a cubic polynomial with the sum, sum of the product of zeroes taken two at a time, and the product of its zeroes as 2,-7,-14 respectively.

Find the sum to n terms of the series 1^2+2^2+3^2-4^2+5^2-6^2+. . . .

The product of n positive numbers is 1, then their sum is a positive integer, that is

CENGAGE-PROGRESSION AND SERIES-Examples
  1. Find the sum of the following series to n terms 5+7+13+31+85+

    Text Solution

    |

  2. Find the sum(k=1)^(oo) sum(n=1)^(oo)k/(2^(n+k)).

    Text Solution

    |

  3. Find the sum of the products of the ten numbers +-1,+-2,+-3,+-4,a n d+...

    Text Solution

    |

  4. Find the sumsum(0leiltjlen)1.

    Text Solution

    |

  5. Let the terms a(1),a(2),a(3),…a(n) be in G.P. with common ratio r. Let...

    Text Solution

    |

  6. Find the sum 1+1/(1+2)+1/(1+2+3)++1/(1+2+3++n)dot

    Text Solution

    |

  7. Find the sum of the series: (1)/((1xx3))+(1)/((3xx5))+(1)/((5xx7)...

    Text Solution

    |

  8. Find the sum to n terms of the series 3//(1^2xx2^2)+5//(2^2xx3^2)+7//(...

    Text Solution

    |

  9. Find the sum to n terms of the series: 1/(1+1^2+1^4)+1/(1+2^2+2^4)+1/...

    Text Solution

    |

  10. Find the sum Sigma(r=1)^(n) r/((r+1)!). Also, find the sum of infinite...

    Text Solution

    |

  11. Find the sum Sigma(r=1)^(n) 1/(r(r+1)(r+2)(r+3)) Also,find Sigma(r=1...

    Text Solution

    |

  12. Find the sum underset(r=1)r(r+1)(r+2)(r+3).

    Text Solution

    |

  13. Find the sum of the series sum(r=11)^(99)(1/(rsqrt(r+1)+(r+1)sqrtr))

    Text Solution

    |

  14. Find the sum of the series 1/(3^2+1)+1/(4^2+2)+1/(5^2+3)+1/(6^2+4)+oo

    Text Solution

    |

  15. Find the sum of first 100 terms of the series whose general term is ...

    Text Solution

    |

  16. Find the sum of the series 2/(1xx3)+5/(2xx3)xx2+(10)/(3xx4)xx2^2+(17)/...

    Text Solution

    |

  17. A long a road lie an odd number of stones placed at intervals of 10 me...

    Text Solution

    |

  18. Prove that x=underset(91 "times")ubrace(1111,....) is composite number...

    Text Solution

    |

  19. If a, b, c are distinct positive real numbers in G.P and logca, logbc,...

    Text Solution

    |

  20. The values of xyz is 15/2 or 18/5 according as the series a, x, y, z, ...

    Text Solution

    |