Question

CMR: 1/2! + 2/3! + 3/4! + 99/100! <1

Giúp mik nha

Ai nhanh nhất mik sẽ tick đó

 

Answer 1

1/2! +2/3! +3/4! +... + 99/100! 
= (1/1! -1/2!) + (1/2! - 1/3!) + (1/3! -1/4!) + .... + (1/99! -1/100!) 
=1 - 1/100! <1 

Answer 2

1/2! +2/3! +3/4! +... + 99/100! 
= (1/1! -1/2!) + (1/2! - 1/3!) + (1/3! -1/4!) + .... + (1/99! -1/100!) 
=1 - 1/100! <1 

Answer 3

1/2! +2/3! +3/4! +... + 99/100! 
= (1/1! -1/2!) + (1/2! - 1/3!) + (1/3! -1/4!) + .... + (1/99! -1/100!) 
=1 - 1/100! <1 

Answer 4

1/2! +2/3! +3/4! +... + 99/100! 
= (1/1! -1/2!) + (1/2! - 1/3!) + (1/3! -1/4!) + .... + (1/99! -1/100!) 
=1 - 1/100! <1 

Answer 5

\(\frac{1}{2!}+\frac{2}{3!}+...+\frac{99}{100!}\)

\(=\frac{2-1}{2!}+\frac{3-1}{3!}+...+\frac{100-1}{100!}\)

\(=\frac{2}{2!}-\frac{1}{2!}+\frac{3}{3!}-\frac{1}{3!}+...+\frac{100}{100!}-\frac{1}{100!}\)

\(=1-\frac{1}{2!}+\frac{1}{2!}-\frac{1}{3!}+...+\frac{1}{99!}-\frac{1}{100!}\)

\(=1-\frac{1}{100!}< 1\)

Answer 6

1/2! +2/3! +3/4! +... + 99/100! 
= (1/1! -1/2!) + (1/2! - 1/3!) + (1/3! -1/4!) + .... + (1/99! -1/100!) 
=1 - 1/100! <1

Answer 7

vì:1/2<1,2/3<1,3/4<1,99/100<1 nên ta có 1/2 + 2/3 + 3/4 +......+ 99/100 < 1