有理数的运算 奥数帮帮忙.拜托各位大神1. 计算:5+5^2+5^3+……+5^n 2. 1/2+(1/4+3/4)+(1/6+3/6+5/6)+……+(1/98+3/98+……+97/98) 3. 1-2/1×(1+2)-3/(1+2)×(1+2+3)-4/(1+2+3)×(1+2+3+4)-……-10/(1+2+3+……+9)×(1+2+3+4+
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![有理数的运算 奥数帮帮忙.拜托各位大神1. 计算:5+5^2+5^3+……+5^n 2. 1/2+(1/4+3/4)+(1/6+3/6+5/6)+……+(1/98+3/98+……+97/98) 3. 1-2/1×(1+2)-3/(1+2)×(1+2+3)-4/(1+2+3)×(1+2+3+4)-……-10/(1+2+3+……+9)×(1+2+3+4+](/uploads/image/z/2501074-10-4.jpg?t=%E6%9C%89%E7%90%86%E6%95%B0%E7%9A%84%E8%BF%90%E7%AE%97+%E5%A5%A5%E6%95%B0%E5%B8%AE%E5%B8%AE%E5%BF%99.%E6%8B%9C%E6%89%98%E5%90%84%E4%BD%8D%E5%A4%A7%E7%A5%9E1.+%E8%AE%A1%E7%AE%97%EF%BC%9A5%2B5%5E2%2B5%5E3%2B%E2%80%A6%E2%80%A6%2B5%5En++2.+1%2F2%2B%281%2F4%2B3%2F4%29%2B%281%2F6%2B3%2F6%2B5%2F6%29%2B%E2%80%A6%E2%80%A6%2B%EF%BC%881%2F98%2B3%2F98%2B%E2%80%A6%E2%80%A6%2B97%2F98%29++3.+1-2%2F1%C3%97%281%2B2%29-3%2F%281%2B2%29%C3%97%281%2B2%2B3%29-4%2F%281%2B2%2B3%29%C3%97%281%2B2%2B3%2B4%29-%E2%80%A6%E2%80%A6-10%2F%281%2B2%2B3%2B%E2%80%A6%E2%80%A6%2B9%EF%BC%89%C3%97%EF%BC%881%2B2%2B3%2B4%2B)
有理数的运算 奥数帮帮忙.拜托各位大神1. 计算:5+5^2+5^3+……+5^n 2. 1/2+(1/4+3/4)+(1/6+3/6+5/6)+……+(1/98+3/98+……+97/98) 3. 1-2/1×(1+2)-3/(1+2)×(1+2+3)-4/(1+2+3)×(1+2+3+4)-……-10/(1+2+3+……+9)×(1+2+3+4+
有理数的运算 奥数帮帮忙.拜托各位大神
1. 计算:5+5^2+5^3+……+5^n 2. 1/2+(1/4+3/4)+(1/6+3/6+5/6)+……+(1/98+3/98+……+97/98) 3. 1-2/1×(1+2)-3/(1+2)×(1+2+3)-4/(1+2+3)×(1+2+3+4)-……-10/(1+2+3+……+9)×(1+2+3+4+……+10) 4. 计算1/2001+2/2001+3/2001+……+2000/2001 5. 已知1/1×2+1/2×3+1/3×4+……+1/n(n+1)大于1921/2001,试求自然数n的最小值是多少? 6.若a1,a2,a3,……都是区间(0,1)中的数,能否找到一个(0,1)中的数,与它们都不相同? 天才帮帮忙,题目看清楚,不要不懂装懂!
有理数的运算 奥数帮帮忙.拜托各位大神1. 计算:5+5^2+5^3+……+5^n 2. 1/2+(1/4+3/4)+(1/6+3/6+5/6)+……+(1/98+3/98+……+97/98) 3. 1-2/1×(1+2)-3/(1+2)×(1+2+3)-4/(1+2+3)×(1+2+3+4)-……-10/(1+2+3+……+9)×(1+2+3+4+
(1) 原式=(5-1)*(1+5+5^2+5^3+…+5^n)/(5-1)-1=(5^(n+1)-1)/4-1 (2)1/2+(1/4+3/4)+(1/6+3/6+5/6)……+(1/98+3/98+……+97/98) =1/2+1+3/2+2+5/2+...+49/2 =(1/2)*(1+2+3+...+49) =(1/2)*(1+49)*49/2 =1225/2. (3)1-1/1*2-2/(1+1)*(1+2)-3/(1+2)*(1+2+3)(1+2+3)-4/(1+2+3)*(1+2+3+4)-.-10/(1+2+3+4+5+6+7+8+9)*(1+2+3+4+5+6+7+8+9+10) =1-(1-1/2)-[1/(1+1)-1/(1+2)]-[1/(1+2)-1/(1+2+3)]-.-[1/(1+2+3+4+5+6+7+8+9)-1/(1+2+3+4+5+6+7+8+9+10)] =1-1+1/2-1/(1+1)+1/(1+2)-(1+2)+1/(1+2+3)-1/(1+2+3)+1/(1+2+3)-.-1/(1+2+3+4+5+6+7+8)+1/(1+2+3+4+5+6+7+8+9)-1/(1+2+3+4+5+6+7+8+9)+1/(1+2+3+4+5+6+7+8+9+10) =1/(1+2+3+4+5+6+7+8+9+10) =1/55 (4)1/2001+2/2001+3/2001+4/2001+``````````+1999/2001+2001/2001=(1+2+3+4+……+2001)/2001=[(1+2000)*2000/2+2001]/2001=1001*2001/2001=1001 (5)原式=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+.+1/n-1/(n+1) =1-1/(n+1)=n/(n+1)〉1921/2001,用1同时减去两边 推出:1/(n+1)