A=1+3/2^3+4/2^4+5/2^5+...100/2^100
1/2*A = 1/2 + 3/2^4 + 4/2^5 +....+ 99/2^100 + 100/2^101
A- A/2 = 1/2A =1/2 + 3/2^3 + 1/2^4 +...+1/2^100 - 100/2^101=
= [1/2+1/2^2 +1/2^3 +...+1/2^100] -100/2^101 (Do 3/2^3 = 1/2^2 +1/2^3)
=[1-(1/2)^101]/(1-1/2) -100/2^101 =
=(2^101 -1)/2^100 - 100/2^101
=> A= (2^101 -1)/2^99 - 100/2^100
tinh a=1+3/2^3+4/2^4+...+100/2^100
Bai 1: Tinh :
A= 1-2+3-4+4-5+...+99-100
B = 1.2+2.3+3.4+4.5+...+99.100
Tính:
\(A=1+\frac{3}{2^3}+\frac{4}{2^4}+\frac{5}{2^5}+...+\frac{100}{2^{100}}\)
Tính A= \(1+\frac{3}{2^3}+\frac{4}{2^4}+\frac{5}{2^5}+....+\frac{100}{2^{100}}\)
Tìm n thuộc Z sao cho \(2n-3⋮n+1\)
Tính
a) A= 1+5+5^2+5^3+.....+5^100
b)B= 1/2+(1/2)^2+(1/2)^3+(1/2)^4+....+(1/2)^99
c)C= (4^5.9^4-2.6^9)/2^10.3^8+6^8.20
tinh 1+3/2^3+4/2^4+...+`00/2^100
1) ( -213) + 186 + ( - 14 ) + 217 + 54 + ( - 49 )
2 ) - 38 . ( 25 - 4 ) + 25 . ( -4 + 38 )
3) -39 . ( 5 - 99 ) + 99 . ( 10 - 39 )
4 ) 1+ 3-5-7+9+ 11 - ....- 397 - 399
5) 1+ 2 + 2^2 + ... + 2 ^ 100
6) 3^102 - 3 ^ 100 - 3 ^ 98 -...3 ^2 - 3 ^0
Tính nhanh:
A = 1/3 - 3/4 - ( - 3/5 ) + 1/72 - 2/9 - 1/36 + 1/15
B = 1/ 5 - 3/7 + 5/9 - 2/11 + 7/13 - 9/16 - 7/13 + 2/11 - 5/9 + 3/7 - 1/5
C = 1/100 - 1/100 . 99 - 1/99 . 98 - 1/98 . 97 - ... - 1/3 . 2 - 1/ 2 . 1
tính tổng 1/2 x ( 1+ 2) + 1/3x( 1+ 2+3) + 1/4 x ( 1+ 2+ 3+ 4) + ...+ 1/100x (n 1+ 2+ 3+ 4+ 5+ ....+ 100)
