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Math Brain Twister

Math Brain Twister - 29 October

100^2 - 99^2 + 98^2 - 97^2 + 96^2 - 95^2 + ... + 2^2 - 1^2 = ?

For Solution : Click Here

5 comments:

  1. x^2-(x-1)^2=2x-1 => x+x-1


    100+99+98+97+96+.......+4+3+2+1=1050

    ReplyDelete
  2. =(100^2-99^2)+(98^2-97^2)+(96^2-95^2)+...........+(4^2-3^2)+(2^2-1^2)

    =[(100+99)(100-99)+(98+97)(98-97)+...............+(4+3)(4-3)+(2+1)(2-1)]

    =199+195+191+.......................+7+3

    Now

    Sum = n/2 (a+L)

    Where

    n=50, a = 199, L = 3

    Sum = 50 / 2 ( 199 + 3)
    =5050

    ReplyDelete
  3. Answer is 5050.
    100^2-99^2 = (99+1)^2-99^2 ->> 99^2+2*99+1-99^2 --> 2*99+1 -->100+99
    Same Way for 98^2-97^2 will give us 98+97
    & so in
    hence total series will read 100+99+98+97+ .....+2+1 : Sum ( 1 to 100)
    Equal 5050.

    ReplyDelete
  4. here is my complicated way ....
    the difference between 2 Results comes from subtracting 2 squared digits is 4 example(100^-99^=199, then 98^-97^=195..then 199-195=4..same when 2^-1^=3,4^-3^=7..then 7-3=4)...
    we have 50 results the lowest is 3 and highest 199 .. if we subtract 3 from all values will get 0, 4::(4*1) ,8::(4*2),12::(4*3)..till 196(4*49) .. then we use::(n^+n)/2 to get total between 1 to 49 ..then multiply it by 4 .. and add 3*(50) to it...will be 4*[(49^+49)/2]+(3*50)=4900 +150=5050.

    ReplyDelete