1/(15*16)+1/(16*17)+1/(17*18)+1/(18*19)+1/(19*20)=?

Question

Математика: 1/(15*16)+1/(16*17)+1/(17*18)+1/(18*19)+1/(19*20)=?

viktordemi2015 · Answer

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

1/(15*16) = 1/15 - 1/16

1/(15*16)+1/(16*17)+1/(17*18)+1/(18*19)+1/(19*20)= 1/15 - 1/16 + 1/16 - 1/17 + 1/17 - 1/18 + 1/18 - 1/19 + 1/19 - 1/20 = 1/15 - 1/20 = 4/60 - 3/60 = 1/60

1/(1516)+1/(1617)+1/(1718)+1/(1819)+1/(19*20)=?

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