1/1x5+1/5x9+1/9x13+……+1/25x29

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1/1x5+1/5x9+1/9x13+……+1/25x29

1/1x5+1/5x9+1/9x13+……+1/25x29
1/1x5+1/5x9+1/9x13+……+1/25x29

1/1x5+1/5x9+1/9x13+……+1/25x29
1/(1×5)+1/(5×9)+...+1/(25×29)
=(1/4)(1-1/5+1/5-1/9+...+1/25-1/29)
=(1/4)(1-1/29)
=(1/4)(28/29)
=7/29
一般的对于正整数n,k
1/[n(n+k)]=(1/k)[1/n -1/(n+k)]

(1/1-1/5)*1/4+(1/5-1/9)*1/4+(1/9-1/13)*1/4+......+(1/25-1/29)*1/4
=(1-1/29)*1/4
=7/29

您看对吗??

公式1/axb=[1/a-1/b)]/(a-b)
1/1x5+1/5x9+1/9x13+……+1/25x29
=[(1-1/5)+(1/5-1/9)+(1/9-1/13)+...(1/25-1/29)]/4
=(1-1/29)/4
=28/(29x4)
=7/29