奥数题求解1/2+1/3+1/4+1/5+..+1/25)+(2/3+2/4+2/5+..+2/25)+(3/4+3/5+3/6+..+3/25)+.1/2+1/3+1/4+1/5+...+1/25)+(2/3+2/4+2/5+.+2/25)+(3/4+3/5+3/6+.+3/25)+)+(23/24+23/25)+24/25
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![奥数题求解1/2+1/3+1/4+1/5+..+1/25)+(2/3+2/4+2/5+..+2/25)+(3/4+3/5+3/6+..+3/25)+.1/2+1/3+1/4+1/5+...+1/25)+(2/3+2/4+2/5+.+2/25)+(3/4+3/5+3/6+.+3/25)+)+(23/24+23/25)+24/25](/uploads/image/z/131235-51-5.jpg?t=%E5%A5%A5%E6%95%B0%E9%A2%98%E6%B1%82%E8%A7%A31%2F2%2B1%2F3%2B1%2F4%2B1%2F5%2B..%2B1%2F25%29%2B%282%2F3%2B2%2F4%2B2%2F5%2B..%2B2%2F25%29%2B%283%2F4%2B3%2F5%2B3%2F6%2B..%2B3%2F25%29%2B.1%2F2%2B1%2F3%2B1%2F4%2B1%2F5%2B...%2B1%2F25%29%2B%282%2F3%2B2%2F4%2B2%2F5%2B.%2B2%2F25%29%2B%283%2F4%2B3%2F5%2B3%2F6%2B.%2B3%2F25%29%2B%29%2B%EF%BC%8823%2F24%2B23%2F25%EF%BC%89%2B24%2F25)
奥数题求解1/2+1/3+1/4+1/5+..+1/25)+(2/3+2/4+2/5+..+2/25)+(3/4+3/5+3/6+..+3/25)+.1/2+1/3+1/4+1/5+...+1/25)+(2/3+2/4+2/5+.+2/25)+(3/4+3/5+3/6+.+3/25)+)+(23/24+23/25)+24/25
奥数题求解1/2+1/3+1/4+1/5+..+1/25)+(2/3+2/4+2/5+..+2/25)+(3/4+3/5+3/6+..+3/25)+.
1/2+1/3+1/4+1/5+...+1/25)+(2/3+2/4+2/5+.+2/25)+(3/4+3/5+3/6+.+3/25)+)+(23/24+23/25)+24/25
奥数题求解1/2+1/3+1/4+1/5+..+1/25)+(2/3+2/4+2/5+..+2/25)+(3/4+3/5+3/6+..+3/25)+.1/2+1/3+1/4+1/5+...+1/25)+(2/3+2/4+2/5+.+2/25)+(3/4+3/5+3/6+.+3/25)+)+(23/24+23/25)+24/25
(1/2+1/3+1/4+…+1/25)+(2/3+2/4+2/5+…2/25)+…+(23/24+23/25)+24/25
=1/2+(1/3+2/3)+(1/4+2/4+3/4)+(1/5+2/5+3/5+4/5)+.+(1/25+2/25+.+24/25)
=1/2+2*3/(2*3)+3*4/(2*4)+4*5/(2*5)+.+24*25/(2*25)
=1/2+2/2+3/2+4/2+.+24/2
=1/2(1+2+3+4+.+24)
=1/2*24*25/2
=150
(1/2+1/3+1/4+...+1/25)+(2/3+2/4+2/5+...+2/25)+(3/4+3/5+3/6+...+3/25)+...+(23/24+23/25)+24/25
=(1/2)+(1/3+2/3)+(1/4+2/4+3/4)+...+(1/24+2/24+...+23/24)+(1/25+2/25+...+24/25)
考察一般项第n项:
1/(n+1...
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(1/2+1/3+1/4+...+1/25)+(2/3+2/4+2/5+...+2/25)+(3/4+3/5+3/6+...+3/25)+...+(23/24+23/25)+24/25
=(1/2)+(1/3+2/3)+(1/4+2/4+3/4)+...+(1/24+2/24+...+23/24)+(1/25+2/25+...+24/25)
考察一般项第n项:
1/(n+1)+2/(n+1)+...+n/(n+1)=(1+2+...+n)/(n+1)=[n(n+1)/2]/(n+1)=n/2
(1/2+1/3+1/4+...+1/25)+(2/3+2/4+2/5+...+2/25)+(3/4+3/5+3/6+...+3/25)+...+(23/24+23/25)+24/25
=(1/2)+(1/3+2/3)+(1/4+2/4+3/4)+...+(1/24+2/24+...+23/24)+(1/25+2/25+...+24/25)
=(1+2+...+24)/2
=24×25/2
=300
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150
数理答疑团为您解答,希望对你有所帮助。
原式=1/2 +(1+2)/3 + (1+2+3)/4 + (1+2+3+4)/5 + ...+ (1+2+3+...+24)/25
=1/2 + 1 + 3/2 + 2 + ...+ 12
=1/2+2/2+3/2+4/2+......+24/2
=1/2 *(1+2+3+4...
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数理答疑团为您解答,希望对你有所帮助。
原式=1/2 +(1+2)/3 + (1+2+3)/4 + (1+2+3+4)/5 + ...+ (1+2+3+...+24)/25
=1/2 + 1 + 3/2 + 2 + ...+ 12
=1/2+2/2+3/2+4/2+......+24/2
=1/2 *(1+2+3+4+...+24)
=1/2 * (1+24)*24/2
=150
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