Question

若an=1的平方+2的平方+3的平方+ +n的平方,则数列3/a1,5/a2,7/a3 , 的前n项和是?

Answer 1

an=1的平方+2的平方+3的平方+ +n的平方=1/6*n(n+1)(2n+1)

数列3/a1,5/a2,7/a3 ,……的通项公式为bn=(2n+1)/an=6/(n(n+1))

S=6/(1*2)+6/(2*3)+6/(3*4)+……+6/(n(n+1))

=6[1/(1*2)+1/(2*3)+1/(3*4)+……+1/(n(n+1))]

=6(1-1/2+1/2-1/3+1/3-1/4+……-1/n+1/n-1/(n+1))

=6(1-1/(n+1))

=6n/(n+1)