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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
- LinaLv 41 decade agoFavorite 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