K = 1 + 2 + 4 + 8 + 16 + 32 +..... + 8192 = ?
K
Khách
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
Những câu hỏi liên quan
22 tháng 7 2015
S = 1 + 2 + 2x2 + 2x2x2 + ... +2x2x..x2 (13 thừ sô nhân 2)
2S = 2 + 2x2 +2x2x2 +..+2x2x2x..x2 (14 thùa số)
2S - S = 2 + 2x 2 + 2x 2x 2 + .. +2x2x2..x2(14 số x2 ) - 1 - 2 - 2x2 - 2x 2 - ... - 2x2x2..x2 ( 13 thừa số nhân 2)
S = 2x2x2x..x2 (14 thùa soos) - 1
S = 16384 - 1 = 16383
14 tháng 8 2016
Gọi dãy số :
2 + 4 + 8 + 16 + 32 +....+ 4096 + 8192 là : A
Đặt A x 2 = 2 + 4 +8 +16 + 32 + ....+ 16384
Cùng thêm 1 và bớt 1 ta có như sau :
A x 2 = 1 + 2 + 4 + 8 + 16 + .....+ 1892 + 16384 - 1
A x 2 = A + 16384 - 1
A = 16384 -1
A = 16383
14 tháng 3 2017
Đặt A = 1 + 2 + 4 + 8 + 16 + … + 4096 + 8192
Ta có: A = 20 + 21 + 22 + 23 + 24 + … + 212 + 213 (1)
Nhân cả hai vế của (1) cho 2, ta được: 2A = 21 + 22 + 23 + 24 + 25 + … + 213 + 214 (2)
Lấy (2) - (1), ta được: 2A - A = 21 + 22 + 23 + 24 + 25 + … + 213 + 214 - (20 + 21 + 22 + 23+ 24 + … + 212 + 213)
A = 21 - 20 + 22 - 21 + 23 - 22 + 24 - 23 + 25 - 24 + … + 213 - 212 + 214 - 213
A = 214 - 20
A = 16384 - 1
A = 16383
NT
2
7 tháng 12 2018
Đặt A = 1 + 2 + 4 + ... + 8192
A = 1 + 2 + 22 + ... + 213
=> 2A = 2 + 22 + 23 + ... + 214
=> 2A - A = ( 2 + 22 + 23 + ... + 214 ) - ( 1 + 2 + 22 + ... + 213 )
<=> A = 214 - 1
<=> A = 16383
Vậy A = 16383
7 tháng 12 2018
16383
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13 tháng 9 2023
A=1+2+2^2+...+2^13
=>2A=2+2^2+...+2^14
=>2A-A=2^14-1
=>A=2^14-1
3 tháng 2 2017
= 1 + 2 + 22 + 23 + ..... + 212 + 213
= 2(1 + 2 + 22 + 23 + ..... + 212 + 213) - (1 + 22 + 23 + 24 + ..... + 212 + 213)
= 2 + 22 + 23 + 24 + .... + 213 + 214 - 1 - 22 - 23 - 24 - ..... - 212 - 213
= 214 - 1
= 16383
