作业帮高一数列数学题.求详细解答,题目如图
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高一数列数学题.求详细解答,题目如图
1.
an=n(n+1)/2=(n²+n)/2
Sn=a1+a2+...+an
=[(1²+2²+...+n²)+(1+2+...+n)]/2
=[n(n+1)(2n+1)/6 +n(n+1)/2]/2
=[n(n+1)(2n+1)+6n(n+1)]/12
=[n(n+1)/12][(2n+1)+6]
=n(n+1)(2n+7)/12
2.
Sn=n(n+1)(2n+7)/12=(2n³+9n²+7n)/12
Tn=S1+S2+...+Sn
=[2(1³+2³+...+n³)+9(1²+2²+...+n²)+7(1+2+...+n)]/12
={2[n(n+1)/2]²+9n(n+1)(2n+1)/6 +7n(n+1)/2}/12
=[n²(n+1)²/2 +3n(n+1)(2n+1)/2 +7n(n+1)/2]/12
=[n(n+1)/24][n(n+1)+3(2n+1)+7]
=[n(n+1)/24](n²+7n+10)
=n(n+1)(n+2)(n+5)/24
an=n(n+1)/2=(n²+n)/2
Sn=a1+a2+...+an
=[(1²+2²+...+n²)+(1+2+...+n)]/2
=[n(n+1)(2n+1)/6 +n(n+1)/2]/2
=[n(n+1)(2n+1)+6n(n+1)]/12
=[n(n+1)/12][(2n+1)+6]
=n(n+1)(2n+7)/12
2.
Sn=n(n+1)(2n+7)/12=(2n³+9n²+7n)/12
Tn=S1+S2+...+Sn
=[2(1³+2³+...+n³)+9(1²+2²+...+n²)+7(1+2+...+n)]/12
={2[n(n+1)/2]²+9n(n+1)(2n+1)/6 +7n(n+1)/2}/12
=[n²(n+1)²/2 +3n(n+1)(2n+1)/2 +7n(n+1)/2]/12
=[n(n+1)/24][n(n+1)+3(2n+1)+7]
=[n(n+1)/24](n²+7n+10)
=n(n+1)(n+2)(n+5)/24