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Solution to math problem?

This is from the Pascal/Cayley math competition preparation questions:

what is the sum of 25/72+25/90+25/110...+25/9900?

I think this has something to do with arithmetic progression?

1 Answer

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  • Lina
    Lv 4
    1 decade ago
    Favorite Answer

    72 = 8*9

    90 =9*10

    110 = 10*11

    9900 =99*100

    of 25/72+25/90+25/110...+25/9900 = 25 Σ 1/((k+7)(k+8)) from k=1 to k = 92

    25 Σ 1/((k+7)(k+8)) = 25 Σ ( 1/(k+7) - 1/(k+8)) = 25 (1/8 -1/9 + 1/9 -1/10 + ...... -1/99 + 1/99 - 1/100)

    = 25 ( 1/8 -1/100) = 23/8 =2.875

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