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Sum of the series S=t^(2) - 2^(2) + 3^(2...

Sum of the series `S=t^(2) - 2^(2) + 3^(2) - 4^(2) + …... - 2002^(2) + 2003^(2)` is

A

`2007006`

B

`1005004`

C

`2000506`

D

`207006`

Text Solution

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The correct Answer is:
A
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Knowledge Check

  • The sum of n terms of the series 1^(2) - 2^(2) + 3^(2)- 4^(2) + 5^(2) -6^(2) + ….is

    A
    `(-1)^(n-1) (n(n+1))/(2)`
    B
    `n(n+1)`
    C
    `-(n+1)n`
    D
    `(n(n+1)(2n+1))/(6)`

  • The sum of first n terms of the series 1^(2) + 2.2^(2) + 3^(2) + 2.4^(2) + 5^(2) + 2.6^(2) + ….is (n(n+1)^(2))/(2) when n is odd the sum is

    A
    `(n(n+1)^(2))/(2)`
    B
    `(n^(2) (n+1))/(2)`
    C
    `(n(n+1)^(2))/(4)`
    D
    `(n^(2) (n+1)^(2))/(4)`

  • The sum of the series 2^(2) + 2(4^(2)) + 3(6^(2)) + ….upto 10 terms is

    A
    11300
    B
    11200
    C
    12100
    D
    12300

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