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-0.25a^4+1/9d^2=100^2-99^2+98^2-97^2+96^2-95^2+…+2^2-1^2
题目详情
-0.25a^4+1/9d^2=
100^2-99^2+98^2-97^2+96^2-95^2+…+2^2-1^2
100^2-99^2+98^2-97^2+96^2-95^2+…+2^2-1^2
▼优质解答
答案和解析
(1) -0.25a^4+1/9d^2
=1/9d^2 -1/4a^4
=(d/3)^2-(a^2/2)^2
=(d/3+a^2/2)(d/3-a^2/2)
(2) 100^2-99^2+98^2-97^2+96^2-95^2+…+2^2-1^2
=(100+99)(100-99)+(98+97)(98-97)+...+(2+1)(2-1)
=100+99+98+97+...+2+1
=(100+1)(100-1+1)/2
=5050
=1/9d^2 -1/4a^4
=(d/3)^2-(a^2/2)^2
=(d/3+a^2/2)(d/3-a^2/2)
(2) 100^2-99^2+98^2-97^2+96^2-95^2+…+2^2-1^2
=(100+99)(100-99)+(98+97)(98-97)+...+(2+1)(2-1)
=100+99+98+97+...+2+1
=(100+1)(100-1+1)/2
=5050
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