A = 1/1×2+1/2×3+1/3×4+…..+1/99×100 Question A = 1/1×2+1/2×3+1/3×4+…..+1/99×100 in progress 0 Môn Toán Sigridomena 4 years 2020-10-31T06:19:26+00:00 2020-10-31T06:19:26+00:00 2 Answers 99 views 0
Answers ( )
Đáp án:
`A=99/100`
Giải thích các bước giải:
`A = 1/(1.2) + 1/(2.3) + 1/(3.4) + . . . + 1/(99.100)`
`A= 1/1-1/2+1/2-1/3+1/3-1/4+….+1/99-1/100`
`A=1-1/100`
`A=99/100`
$A$ $=$ $\frac{1}{1.2}$ $+$ $\frac{1}{2.3}$ $+$ $\frac{1}{3.4}$ $+$ $…$ $+$ $\frac{1}{99.100}$
$=$ $1$ $-$ $\frac{1}{2}$ $+$ $\frac{1}{2}$ $-$ $\frac{1}{3}$ $+$ $\frac{1}{3}$ $-$ $\frac{1}{4}$ $+$ $…$ $+$ $\frac{1}{9}$ $-$ $\frac{1}{100}$
$=$ $1$ $-$ $\frac{1}{100}$ $=$ $\frac{99}{100}$