计算:1눀-2눀+3눀-4눀+5눀-6눀+7눀-8눀+9눀-10눀=

2025-02-27 13:11:12
推荐回答(3个)
回答1:

n²-(n+1)²=(n+n+1)(n-n-1)=-(2n+1}
∴1²-2²+3²-4²+5²-6²+7²-8²+9²-10²
=-(2*1+1)-(2*3+1)-(2*5+1)-(2*7+1)-(2*9+1)
=-2(1+3+5+7+9)-5
=-2*25-5
=-55

回答2:

(1²-2²)+(3²-4²)+(5²-6²)+(7²-8²)+(9²-10²)
= -(1+2)-(3+4)-(5+6)-(7+8)-(9+10)
=-55

回答3:

1-4+9-16+25-36+49-64+81-100=(1+9+25+49+81)-(4+16+36+64+100)=165-240=-75