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222-9+11+12:2*14+14 = ? ( )

## Toán Lớp 7: 1/2 chấm than + 2/3 chấm than + 3/4 chấm than + –+ 99/100 chấm than <1

Toán Lớp 7: 1/2 chấm than + 2/3 chấm than + 3/4 chấm than + ……..+ 99/100 chấm than <1

## Comments ( 2 )

1. Ta có : 1/(2!)+2/(3!)+3/(4!)+….+99/(100!)
=(2-1)/(2!)+(3-1)/(3!)+(4-1)/(4!)+…+(100-1)/(100!)
=2/(2!)-1/(2!)+3/(3!)-1/(3!)+4/(4!)-1/(4!)+…+100/(100!)-1/(100!)
=1/(1!)-1/(2!)+1/(2!)-1/(3!)+1/(3!)-1/(4!)+…+1/(99!)-1/(100!)
=1-1/(100!)
Vì 1-1/(100!)<1 =>1/(2!)+2/(3!)+3/(4!)+….+99/(100!)<1(đpcm)

2. Giải đáp + Lời giải và giải thích chi tiết:
\frac{1}{2!}+\frac{2}{3!}+\frac{2}{3!}+\frac{3}{4!}+…+\frac{99}{100!}
=\frac{2-1}{2!}+\frac{3-1}{3!}+\frac{4-1}{3!}+…+\frac{100-1}{100!}
=\frac{2}{2!}-\frac{1}{2!}+\frac{3}{3!}-\frac{1}{3!}+\frac{4}{4!}+…+\frac{100}{100!}-\frac{1}{100!}
=\frac{1}{1!}-\frac{1}{2!}+\frac{1}{2!}-\frac{1}{3!}+\frac{1}{3!}-\frac{1}{4!}+..+\frac{1}{99!}-\frac{1}{100!}
=1-\frac{1}{100}<1
text{#Study Well}