计算1)（2+1)(2^2 +1)(2^4 +1).(2^2n +1)2)100^2-99^2+98^2-97^2+96

来源：学生作业帮编辑：神马作文网作业帮分类：数学作业时间：2024/11/20 00:11:03

计算
1)（2+1)(2^2 +1)(2^4 +1).(2^2n +1)
2)100^2-99^2+98^2-97^2+96^2-95^2+.+2^2-1^2
3)（1-1/2^2)(1-1/3^2)(1-1/4^2).(1-1/9^2)(1-1/10^2)
4) (y-1/2)^2
5)(2x+3y)^2-(4x-9y)(4x+9y)+(2x-3y)^2
6) 1.2345^2+0.7655^2+2.469*0.7655
7) (x+2y)(x-y)-(x+y)^2
先化简后求值
1）(x+y)+(2x+y/1*2)+(3x+y/2*3)+.+(9x+y/8*9) x=2 ,y=9

(1)原式=(2-1)*(2+1)*(2^2+1)*(2^4+1)*……*(2^n+1)
=(2^2-1*(2^2+1)*(2^4+1)*……*(2^n+1)
=（2^4-1)(2^4+1)*……*(2^n+1)
=(2^n+1)(2^n-1)
=2^2n-1
(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+…………+3+2+1=5050
1992^2-1993乘1991=
=1992×1992-（1992+1）（1992-1）
=1992×1992-（1992×1992-1×1）
=1
(3)(1-1/2^2)(1-1/3^2)(1-1/4^2).(1-1/9^2)(1-1/10^2)
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)……(1-1/10)(1+1/10)
=(1/2)(3/2)(2/3)(4/3)……(9/10)(11/10)
中间约分约掉了
=(1/2)*(11/10)
=11/20
(4)(y-1/2)^2
=y^2-y+1/4
(5)(2x+3y)^2-(4x-9y)(4x+9y)+(2x-3y)^2
=4x^2+12xy+9y^2-16x^2+81y^2+4x^2-12xy+9y^2
=-8x^2+99y^2
(6)1.2345^2+0.7655^2+2.469*0.7655
=1.2345^2+2*1.2345*0.7655+0.7655^2
=(1.2345+0.7655)^2
=2^2
=4
(7)原式 = x^2-xy+2xy-2y^2-(x^2+2xy+y^2)
= -xy-3y^2
1)（x+y)+(2x+y/1*2)+(3x+y/2*3)+.+(9x+y/8*9)
=(x+2x+3x+...+9x)+(y+y/1*2+y/2*3+...+y/8*9)
=(1+9)*9x/2 +[y+(y-y/2)+(y/2-y/3)+(y/3-y/4)+...+(y/8-y/9)]
=45x+(8/9)y
代入 x=2 ,y=9
原式=98

计算：n(n+1)(n+2)(n+3)+1 计算级数 ∑n/2^(n-1) 计算9^n*(1/27)^n+1*3^n+2 计算：C(1,n)+2C(2,n)+3C(3,n) + … + nC(n,n) 简便方法计算：1/n+1+1/n+2+1/n+3+1/n+4+…+1/n+100 计算(-m+1/2n^2)^2 如果,n是大于2的整数,计算1/(n-1)(n-2)+1/(n-2)(n-3)+1/(n-3)(n-4)+……+1/(n 计算:(m+1/2n)(-m+1/2n) 计算1/(m-n)-1/(m+n)-2n/(m^2+n^2)-4n^3/(m^4+n^4)-8n^7/(m^8+n^8) (2m+1/3n)^2 计算计算：limn^2[(k/n)-(1/n+1)-(1/n+2)-……-(1/n+k)] 1+2+3+...+(n-1）+n计算方式