数学(平方差)1.100^2-99^2+98^2-97^2+96^2-95^2+.2^2-2^1:2.(a+1)(a^2+1)(a^4+1)...(a^1024+1)其中a不等于1.计算这两题.必须有过程(简便)答得好的加分
数学(平方差)
1.100^2-99^2+98^2-97^2+96^2-95^2+.2^2-2^1:
2.(a+1)(a^2+1)(a^4+1)...(a^1024+1)其中a不等于1.
计算这两题.必须有过程(简便)
答得好的加分
1.原式=(100+99)*(100-99)+(98-97)*(98+97)+(96+95)*(96-95)+.....+(2+1)*(2-1)=100+99+98+97+96+95+……+2+1=101×50=5050
2.原式=(a-1)(a+1)(a^2+1)(a^4+1)...(a^1024+1)÷(a-1)=(a^2-1)(a^2+1)(a^4+1)...(a^1024+1)÷(a-1)=(a^4-1)(a^4+1)......(a^1024+1)÷(a-1)=(a^2048+1)/(a-1)
原式=(100+99)*(100-99)+(98-97)*(98+97)+(96+95)*(96-95)+.....+(2+1)*(2-1)=100+99+98+97+96+95+……+2+1=101×50=5050
原式=.(a+1)(a^2+1)(a^4+1)...(a^1024+1)乘以(a-1)除以(a-1)
=(a-1)(a+1)(a^2+1)(a^4+1)...(a^1024+1)/(a-1)
=(a^2-1)(a^2+1)(a^4+1)...(a^1024+1)/(a-1)
=(a^2048-1)/(a-1)
1、参考公式X2-Y2=(x-y)*(x+y),那么1式=100+99+98.........+3+2+1=100+50+(99+1)+(98+2)...+(49+51)=100+50+49*100=你说呢?
2、参考他们的就对了,也有运用到上面公式X2-Y2,
1原式=(100-99)(100+99)+(98-97)(98+97)+(96-95)(96+95)+......(2-1)(2+1)=199+195+191+......+3=(199+3)/2*50=101*50=5050
1 、原式=(100+99)*(100-99)+(98+97)*(98-97)……+(1+2)*(2-1)
=199+195+……+3
=(199+3)*50/2=5050(高斯求和)
2、原式=.(a+1)(a^2+1)(a^4+1)...(a^1024+1)乘以(a-1)除以(a-1)
=(a-1)(a+1)(a^2+1)(a^4+1)...(a^1024+1)/(a-1)
=(a^2-1)(a^2+1)(a^4+1)...(a^1024+1)/(a-1)……
就等于=(a^2048-1)/(a-1)