Question

Arătați ca 1/n-1/n+1=1/n•(n+1). Ex 16

Answer 1

16

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

a) S= 1/1-1/2+1/2-1/3+1/3-1/4+....+1/89-1/90 = 1-1/90=89/90

c)S=1/4-1/5+1/5-1/6+...1/71-1/72=1/4-1/72=(18-1)/72=19/72

17

S=1/(1·2)+1/(2·3)+1/(3·4)+....+1/(9·10) = 1-1/10=9/10