数学的数列问题,请详细说明一下,快一点,谢谢在数列(an)中,若a1+2a2+3a3+……nan=n(n+1)(n+2),则an=?答案是2n/n+1谢谢找到答案了a1+2a2+3a3+……+(n-1)a(n-1)=(n-1)n(n+1) 两式相减,nan=3n(n+1) 于是an=3n+3
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![数学的数列问题,请详细说明一下,快一点,谢谢在数列(an)中,若a1+2a2+3a3+……nan=n(n+1)(n+2),则an=?答案是2n/n+1谢谢找到答案了a1+2a2+3a3+……+(n-1)a(n-1)=(n-1)n(n+1) 两式相减,nan=3n(n+1) 于是an=3n+3](/uploads/image/z/400158-54-8.jpg?t=%E6%95%B0%E5%AD%A6%E7%9A%84%E6%95%B0%E5%88%97%E9%97%AE%E9%A2%98%2C%E8%AF%B7%E8%AF%A6%E7%BB%86%E8%AF%B4%E6%98%8E%E4%B8%80%E4%B8%8B%2C%E5%BF%AB%E4%B8%80%E7%82%B9%2C%E8%B0%A2%E8%B0%A2%E5%9C%A8%E6%95%B0%E5%88%97%EF%BC%88an%29%E4%B8%AD%2C%E8%8B%A5a1%2B2a2%2B3a3%2B%E2%80%A6%E2%80%A6nan%3Dn%28n%2B1%29%28n%2B2%29%2C%E5%88%99an%3D%3F%E7%AD%94%E6%A1%88%E6%98%AF2n%2Fn%2B1%E8%B0%A2%E8%B0%A2%E6%89%BE%E5%88%B0%E7%AD%94%E6%A1%88%E4%BA%86a1%2B2a2%2B3a3%2B%E2%80%A6%E2%80%A6%2B%28n-1%29a%28n-1%29%3D%28n-1%29n%28n%2B1%29+%E4%B8%A4%E5%BC%8F%E7%9B%B8%E5%87%8F%EF%BC%8Cnan%EF%BC%9D3n%28n%2B1%29+%E4%BA%8E%E6%98%AFan%EF%BC%9D3n%2B3)
数学的数列问题,请详细说明一下,快一点,谢谢在数列(an)中,若a1+2a2+3a3+……nan=n(n+1)(n+2),则an=?答案是2n/n+1谢谢找到答案了a1+2a2+3a3+……+(n-1)a(n-1)=(n-1)n(n+1) 两式相减,nan=3n(n+1) 于是an=3n+3
数学的数列问题,请详细说明一下,快一点,谢谢
在数列(an)中,若a1+2a2+3a3+……nan=n(n+1)(n+2),则an=?
答案是2n/n+1谢谢
找到答案了
a1+2a2+3a3+……+(n-1)a(n-1)=(n-1)n(n+1)
两式相减,nan=3n(n+1)
于是an=3n+3
数学的数列问题,请详细说明一下,快一点,谢谢在数列(an)中,若a1+2a2+3a3+……nan=n(n+1)(n+2),则an=?答案是2n/n+1谢谢找到答案了a1+2a2+3a3+……+(n-1)a(n-1)=(n-1)n(n+1) 两式相减,nan=3n(n+1) 于是an=3n+3
由a(1)+2a(2)+3a(3)+……na(n)=n(n+1)(n+2)求出一些项观察一下:
a(1)=6=3(1+1)
a(2)=9=3(2+1)
a(3)=12=3(3+1)
a(4)=15=3(4+1)
所以,猜测
a(n)=3(n+1)
证明
当n=1时
a(1)=6=1*(1+1)*(1+2),正确
假设n=k时正确,即
a(1)+2a(2)+3a(3)+……ka(k)=k(k+1)(k+2)
当n=k+1时
a(1)+2a(2)+3a(3)+……ka(k)+(k+1)a(k+1)=
=k(k+1)(k+2)+(k+1)*3(k+1+1)=
=k(k+1)(k+2)+(k+1)*3(k+2)=
=(k+1)(k+2)(k+3)=
=(k+1)[(k+1)+1][(k+1)+2]
正确!