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求和,1^2/(1^2+10^2)+2^2/(2^2+9^2)+3^2/(3^2+8^2)+...+10^2/(10^2+1^2)
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求和,1^2/(1^2+10^2)+2^2/(2^2+9^2)+3^2/(3^2+8^2)+...+10^2/(10^2+1^2)
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答案和解析
1^2/(1^2+10^2)+2^2/(2^2+9^2)+3^2/(3^2+8^2)+...+10^2/(10^2+1^2)
=[1-10^2/(1^2+10^2)]+[1-9^2/(2^2+9^2)]+...+[1-1^2/(10^2+1^2)]
=10-(10^2+1^2)/(10^2+1^2) - (9^2+2^2)/(9^2+1^2)- (8^2+3^2)/(8^2+3^2)
-(7^2+4^2)/(7^2+4^2) - (6^2+5^2)/(6^2+5^2)
=10-5
=5
=[1-10^2/(1^2+10^2)]+[1-9^2/(2^2+9^2)]+...+[1-1^2/(10^2+1^2)]
=10-(10^2+1^2)/(10^2+1^2) - (9^2+2^2)/(9^2+1^2)- (8^2+3^2)/(8^2+3^2)
-(7^2+4^2)/(7^2+4^2) - (6^2+5^2)/(6^2+5^2)
=10-5
=5
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