`text(B)=1/2+1/2^2+1/2^3+...+1/2^100`
`=>text(2B)=2.(1/2+1/2^2+1/2^3+...+1/2^100)`
`=>text(2B)=1+1/2+1/2^2+...+1/2^99`
`=>text(2B)-text(C)=(1+1/2+1/2^2+...+1/2^99)-(1/2+1/2^2+1/2^3+...+1/2^100)`
`=>text(B)=1-1/2^100`
1)Tính nhanh: A=1+3+3^2+3^3+3^4+...+3^100
B= 1+4^2+4^4+4^6+...+4^100
2) Cho biết 1^2+2^3+3^2+4^2+...+10^2= 385
Tính a) S1= 2^2+4^2+...+20^2
. b) S2= 100^2+200^2+...1000^2
CMR : a) 1/2! + 2/3! + 3/4! +...+ 99/100! < 1
b) 1.2-1/2! + 2.3-1/3! + 3.4-1/4! +...+ 99.100-1/100! < 2
A = \(\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+......+\dfrac{1}{2^{100}}\)
B = \(\dfrac{1}{2^2}+\dfrac{1}{3^2}+\dfrac{1}{4^2}+....+\dfrac{1}{100^2}\)
mk cần gấp
10 Rút gọn:
a) A= 1+2+22+23+24+...+249+250
b) B= \(\dfrac{1}{2}+(\dfrac{1}{2})^2+(\dfrac{1}{2})^3+(\dfrac{1}{2})^4+(\dfrac{1}{2})^5+...+(\dfrac{1}{2})^{99}+(\dfrac{1}{2})^{100}\)
Tính:
\(B=3+\dfrac{3}{1+2}+\dfrac{3}{1+2+3}+........+\dfrac{3}{1+2+.....+100}\)
Bài 1: Tính:
a) A= 3100 - 399 + 398 - 397 +...+ 32 - 3 +1
b) B= 2100 - 299 + 298 - 297 +...+ 22 -2
A=(1/2^2-1)*(1/3^2-1)*(1/4^2-1)...(1/100^2-1)
CM: S= 1+1/2^2+1/3^2+......+1/100^2 <2
*Rút gọn
1) G=\(\dfrac{2}{3}+\dfrac{2}{3^3}+\dfrac{2}{3^5}+...+\dfrac{2}{3^{99}}\)
2) H=\(\dfrac{1}{2}-\dfrac{1}{2^4}+\dfrac{1}{2^7}-\dfrac{1}{2^{16}}+...-\dfrac{1}{2^{58}}\)
3) E=\(\dfrac{-1}{3}+\left(\dfrac{-1}{3}\right)^2+\left(\dfrac{-1}{3}\right)^3+...+\left(\dfrac{-1}{100}\right)^{100}\)
rút gọn A= 1+1/2+3/2^3+4/2^4+5/2^5+....+100/2^100
