求数列1/（3*5）,1/（5*7）,1/（7*9）.的前N项和 3*5是:3乘以5的意思
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an = 1/(2n+1)(2n+3)
1/（3*5）=1/2*(1/3 - 1/5)
1/（5*7）=1/2*(1/5 - 1/7)
1/（7*9）=1/2*(1/7 - 1/9)
...
aN-1 = 1/(2N-1)(2N+1) = 1/2(1/(2N-1) - 1/(2N+1)
aN = 1/(2N+1)(2N+3) = 1/2(1/(2N+1) - 1/(2N+3))
所以的前N项和
=a1 + a2 +...+aN-1 + aN
=1/2(1/3 - 1/(2N+3))
=N/3(2N+3))
1/（3*5）=1/2*(1/3 - 1/5)
1/（5*7）=1/2*(1/5 - 1/7)
1/（7*9）=1/2*(1/7 - 1/9)
...
aN-1 = 1/(2N-1)(2N+1) = 1/2(1/(2N-1) - 1/(2N+1)
aN = 1/(2N+1)(2N+3) = 1/2(1/(2N+1) - 1/(2N+3))
所以的前N项和
=a1 + a2 +...+aN-1 + aN
=1/2(1/3 - 1/(2N+3))
=N/3(2N+3))
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