等差数列 中,若a1=1 ,a8=15 ,则1/a1·a2+1/a2·a3 +… +1/a100·a101=?

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等差数列 中,若a1=1 ,a8=15 ,则1/a1·a2+1/a2·a3 +… +1/a100·a101=?

等差数列 中,若a1=1 ,a8=15 ,则1/a1·a2+1/a2·a3 +… +1/a100·a101=?
等差数列 中,若a1=1 ,a8=15 ,则1/a1·a2+1/a2·a3 +… +1/a100·a101=?

等差数列 中,若a1=1 ,a8=15 ,则1/a1·a2+1/a2·a3 +… +1/a100·a101=?
a1=1,a8=15,则:an=2n-1
则:1/[(an)(a(n+1))=1/[(2n-1)(2n+1)]=(1/2)[1/(2n+1)-1/(2n-1)]
则原式=(1/2)[1/1-1/201]=100/201