采取求通项的办法.
An=3/n(n+1)=3[1/n - 1/(n+1)]
那么,有:
A1=3(1/1 – 1/2)
A2=3(1/2 – 1/ 3)
A3=3(1/3 – 1/4)
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An=3[1/n – 1/(n+1)]
从而,项数和是sn为:
Sn=3[(1/1 – 1/2)+( 1/2 – 1/ 3)+( 1/3 – 1/4) +……+(1/n – 1/(n+1))]
=3[1 - 1/2 + 1/2 - 1/3 + 1/3 – 1/4 +……+1/n – 1/(n+1)]
=3[1 – 1/(n+1)]
=3n/(n+1)
所以,S5=3*5/(5+1)
=15/6
=5/2