图片插不成功- =求lim{3/(1^2*2^2)+5/(2^2乘以3^2)+……+(2n+1)/n^2*(n+1)^2
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图片插不成功- =求lim{3/(1^2*2^2)+5/(2^2乘以3^2)+……+(2n+1)/n^2*(n+1)^2}
![图片插不成功- =求lim{3/(1^2*2^2)+5/(2^2乘以3^2)+……+(2n+1)/n^2*(n+1)^2](/uploads/image/z/8001161-17-1.jpg?t=%E5%9B%BE%E7%89%87%E6%8F%92%E4%B8%8D%E6%88%90%E5%8A%9F-+%3D%E6%B1%82lim%7B3%2F%281%5E2%2A2%5E2%29%2B5%2F%282%5E2%E4%B9%98%E4%BB%A53%5E2%29%2B%E2%80%A6%E2%80%A6%2B%282n%2B1%29%2Fn%5E2%2A%28n%2B1%29%5E2)
题呢?
再问: 有了。。
再答: lim(n→∞){3/(1^2*2^2)+5/(2^2×3^2)+……+(2n+1)/n^2*(n+1)^2}=lim(n→∞){(2²-1²)/(1^2*2^2)+(3²-2²)/(2^2×3^2)+……+((n+1)²-n²)/(n^2*(n+1)^2)}=lim(n→∞){1-1/2²+1/2²-1/3²+……+1/n²-1/(n+1)²}=lim(n→∞){1-1/(n+1)²)=1
再问: 有了。。
再答: lim(n→∞){3/(1^2*2^2)+5/(2^2×3^2)+……+(2n+1)/n^2*(n+1)^2}=lim(n→∞){(2²-1²)/(1^2*2^2)+(3²-2²)/(2^2×3^2)+……+((n+1)²-n²)/(n^2*(n+1)^2)}=lim(n→∞){1-1/2²+1/2²-1/3²+……+1/n²-1/(n+1)²}=lim(n→∞){1-1/(n+1)²)=1
图片插不成功- =求lim{3/(1^2*2^2)+5/(2^2乘以3^2)+……+(2n+1)/n^2*(n+1)^2
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