数学计算,要求将清楚过程(1+1×3/1)×(1+2×4/1)×(1+3×5/1)×(1+4×6/1)…×(1+97×99/1)×(1+98×100/1)=多少
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![数学计算,要求将清楚过程(1+1×3/1)×(1+2×4/1)×(1+3×5/1)×(1+4×6/1)…×(1+97×99/1)×(1+98×100/1)=多少](/uploads/image/z/2743227-27-7.jpg?t=%E6%95%B0%E5%AD%A6%E8%AE%A1%E7%AE%97%2C%E8%A6%81%E6%B1%82%E5%B0%86%E6%B8%85%E6%A5%9A%E8%BF%87%E7%A8%8B%EF%BC%881%2B1%C3%973%2F1%29%C3%97%281%2B2%C3%974%2F1%29%C3%97%281%2B3%C3%975%2F1%29%C3%97%281%2B4%C3%976%2F1%29%E2%80%A6%C3%97%281%2B97%C3%9799%2F1%29%C3%97%281%2B98%C3%97100%2F1%29%3D%E5%A4%9A%E5%B0%91)
数学计算,要求将清楚过程(1+1×3/1)×(1+2×4/1)×(1+3×5/1)×(1+4×6/1)…×(1+97×99/1)×(1+98×100/1)=多少
数学计算,要求将清楚过程
(1+1×3/1)×(1+2×4/1)×(1+3×5/1)×(1+4×6/1)…×(1+97×99/1)×(1+98×100/1)=多少
数学计算,要求将清楚过程(1+1×3/1)×(1+2×4/1)×(1+3×5/1)×(1+4×6/1)…×(1+97×99/1)×(1+98×100/1)=多少
an=1+1/[n*(n+2)]=[n(n+2)+1]/[n(n+2)]=(n+1)^2/[n(n+2)] n=1,2,3.
a1=2^2/(1*3)
a2=3^2/(2*4)
a3=4^2/(3*5)
a4=5^2/(4*6)
.
a98=99^2/(98*100)
注:a1*a2*a3*a4=2*5/6 a2的3的平方可以与a1和a3的分母的3可以约掉,依次内推
a1a2a3...a98=2*99/100=1.98
分母写反了吧?是(1+1*1/3)*(1+2*1/4)……*(1+98*1/100)吧?
我就按这个解答了。
通项是1+n*1/(n+2)=(2n+2)/(n+2)=2*(n+1)/(n+2)
所以原试=2*[2/3* 3/4* 4/5 * ……98/99 * 99/100]=2*[2/100]=1/25不对吧,标准答案上是1.98.我搞不清什么状况唔。。。。我错了。那个2...
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分母写反了吧?是(1+1*1/3)*(1+2*1/4)……*(1+98*1/100)吧?
我就按这个解答了。
通项是1+n*1/(n+2)=(2n+2)/(n+2)=2*(n+1)/(n+2)
所以原试=2*[2/3* 3/4* 4/5 * ……98/99 * 99/100]=2*[2/100]=1/25
收起
3/1=3, 4/1=4 ?
an=1+n/(n+2)=2*(n+1)/(n+2) (n=1,2,3...98)
sn=(2*2/3)*(2*3/4)*(2*4/5*)...*(2*99/100)
=2^98*(2/3)*(3/4)*(4/5)*....*(99/100)
=2^98*(2/100)
=(2^99)/100