Question

[Vũ Hương Giang]

Tính nhanh: 

\(\frac{1}{1+2}+\frac{1}{1+2+3}+\frac{1}{1+2+3+4}+.......+\frac{1}{1+2+3+4+....+15}\)

THANKS

Answer 1

[Lãnh Hạ Thiên Băng]

1/1+2 + 1/1+2+3 +1/1+2+3+4 +...+1/1+2+3+...+50

Ta có 2/2(1+2)+2/2(1+2+3)+...+2/2(1+2+...+50)

=2/6+2/12+2/20+...+2/2550

=2/2.3+2/3.4+...+2/50.51

=2(1/2.3+1/3.4+...+1/50.51)

=2(1/1-1/2+1/2-...+1/50-1/51)

=2.(1-1/51)

=2.50/51=100/51