Question

Tính

a) A=1/2 +1/6 + 1/12 + 1/20 + 1/30 + ....+ 1/9900

b) B= 3,78(200-68)-3,78(100-68)

Answer 1

Lời giải:

a.

$A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}$

$A=\frac{2-1}{1.2}+\frac{3-2}{2.3}+\frac{4-3}{3.4}+...+\frac{100-99}{99.100}$

$=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{99}-\frac{1}{100}$

$=1-\frac{1}{100}=\frac{99}{100}$

b.

$B=3,78[(200-68)-(100-68)]$

$=3,78.100=378$

Answer 2

a) A=\(\dfrac{1}{1.2}\)+\(\dfrac{1}{2.3}\)+\(\dfrac{1}{3.4}\)+...+\(\dfrac{1}{99.100}\)
A= 1-\(\dfrac{1}{2}\)+\(\dfrac{1}{2}\)-\(\dfrac{1}{3}\)+\(\dfrac{1}{3}\)-\(\dfrac{1}{4}\)+...+\(\dfrac{1}{99}\)-\(\dfrac{1}{100}\)
A= 1-\(\dfrac{1}{100}\)
A= \(\dfrac{99}{100}\)