计算 (2²+4²+6²+...+50²)-(1²+3²+5²+...+49²)
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![计算 (2²+4²+6²+...+50²)-(1²+3²+5²+...+49²)](/uploads/image/z/763455-39-5.jpg?t=%E8%AE%A1%E7%AE%97+%EF%BC%882%26%23178%3B%2B4%26%23178%3B%2B6%26%23178%3B%2B...%2B50%26%23178%3B%EF%BC%89-%EF%BC%881%26%23178%3B%2B3%26%23178%3B%2B5%26%23178%3B%2B...%2B49%26%23178%3B%EF%BC%89)
计算 (2²+4²+6²+...+50²)-(1²+3²+5²+...+49²)
计算 (2²+4²+6²+...+50²)-(1²+3²+5²+...+49²)
计算 (2²+4²+6²+...+50²)-(1²+3²+5²+...+49²)
(2²+4²+6²+...+50²)-(1²+3²+5²+...+49²)
=2²-1²+4²-3²+6²-5²+...+50²-49²
=(2+1)(2-1)+(4+3)(4-3)+(6+5)(6-5)+...+(50+49)(50-49)
=1+2+3+4+5+6+...+49+50
=(1+50)×25
=1275
(2²+4²+6²+...+50²)-(1²+3²+5²+...+49²)
=(2^2-1^2)+(4^2-3^2)+...+(50^2-49)^2
=(2+1)(2-1)+(4+3)(4-3)+...+(50+49)(50-49)
=1+2+3+4+...+49+50
=50*(50+1)/2
=1275
2-1=1.25X1=25