Question

a= 1/1x2+1/2x3+....+1/n(n+1)
a=0,999
n>=1
n=?

Answer 1

1/1*2=1-1/2
1/2*3=1/2-1/3
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1/n*(n+1)=1/n-1/(n+1)    Se    aduna     sin-n   stanga    si-n   dreapta   si    se    obtine
1/1*2+1/2*3+...1/n*(n+1)=1-1/2+1/2-1/3+....1/n-1-1/(n+1)=1-1/(n+1)
1-1/(n+1)=0,999
n+1-1)/(n+1)=0.999
n/(n+1)=999/1000=>n+1=1000=> n=999