2100 = (210)10 = 102410 > 100010 = 1030
2100 = 231 . 26 . 263 = 231 . 64 . 5127 < 231 . 125 . 6257 = 231 . 53 . (54)7 = 231 . 531 = 1031
1030 < 2100 < 1031
vậy 2100 có 31 chữ số
co
31 chu so cac p a
cho minh DUNG NHE
Ta có:2^10=1024>10^3=>2^100>10^30 (1)
Mặt khác:2^10=1024 <1025=>2^100<1025^10
=>2^100/10^30 =(2^10/10^3)^10 < (1025/10^3)^10=(41/40)^10
Ta đã biết 0<b<a thì ab+b<ab+a
=>b(a+1) <a(b+1) =>a+1/b+1<a/b (*)
Áp dụng (*) ta có:41/40<40/39<39/38<....<32/31<31/30
Do đó:2^100/10^30 <(41/40)^10<40/39.39/38......31/30=4/3<2
Suy ra:2^100<2.10^3 (2)
Vậy 2^100 có 31 chữ số
2100 = (210)10 = 102410 > 100010 = 1030
2100 = 231 . 26 . 263 = 231 . 64 . 5127 < 231 . 125 . 6257 = 231 . 53 . (54)7 = 231 . 531 = 1031
1030 < 2100 < 1031
vậy 2100 có 31 chữ số
5 mu 100 co bao nhieu chu so trong he thap phan
= 31 nhưng tớ vẫn chưa hiểu vì sao đc 31
2^100=(2^10)^10=1024^10>1000^10=10^30
2^100=2^31.2^6.2^63=2^31.64.512^7<2^31.125.625^7=2^31.5^3.(5^4)^7=2^31.%^31=10^31</p>
10^30<2^100<10^31</p>
=> 2^100 có 31 chữ số
-------------
CM: có 2^10 = 1024
=> 2^100 = (2^10)^10 = 1024^10 = (1000 + 24)^10 =
= 1000^10 + ... (10Ck).1000^k.24^(10-k) .. + 24^10
<<với (k = 1,2,..9)>>
có thể cm tổng của các (10Ck).1000^k.24^(10-k) < 1000^10
<<khai triển tường minh tổ hợp và đánh giá theo số hạng lớn nhất, có lẻ ko cần thiết cm dài dòng>>
=> số chữ số của 2^100 = số chữ số của 1000^10 = 10^30
=> có 31 chữ số (trong 10^30 có: 1 chữ số 1 và 30 chữ số 0)
31 chứ 30 gì
3 100% không 1000000000000000% luôn
có tất cả là 31 chữ số bạn nhé
chúc bạn thành công
Mình đang ôn thi Hsg mệttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttt
Ta có:
2100 = (210)10 = 102410 > 100010 = 1030
Mặt khác:
2100 = 231 . 26 . 263 = 231 . 64 . 29.7
= 231 . 64 . (29)7
= 231 . 64 . 5127
< 231 . 125 . 6257
= 231 . 53 . (54)7
= 231 . 53 . 54.7
= 231. 53 . 528
= 231 . 53+28
= 231 . 531 = (2 .5 )31 = 1031
Ta thấy 1030 là số nhỏ nhất có 31 chữ số và 1031 là số nhỏ nhất có 32 chữ số; mà 1030 < 2100 <1031
=> 2100 có 31 chữ số.
