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\(S=\left(1+4\right)+\left(4^2+4^3\right)+...+\left(4^{98}+4^{99}\right)\\ S=\left(1+4\right)+4^2\left(1+4\right)+...+4^{98}\left(1+4\right)\\ S=\left(1+4\right)\left(1+4^2+...+4^{98}\right)=5\left(1+4^2+...+4^{98}\right)⋮5\)
\(S=\left(1+4\right)+...+4^{98}\left(1+4\right)\)
\(=5\left(1+...+4^{98}\right)⋮5\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có:
7245 - 7244 = 7244.(72 - 1) = 7244.71
7244 - 7243 = 7243.(72 - 1) = 7243.71
Vì 7244.71 > 7243.71
=> 7245 - 7244 > 7244 - 7243
Ta có:
\(72^{45}-72^{44}=72^{44}\left(72-1\right)=72^{44}.71\)
\(72^{44}-72^{43}=72^{43}\left(72-1\right)=72^{43}.71\)
Vì \(72^{44}.71>72^{43}.71\) nên \(72^{45}-72^{44}>72^{44}-72^{43}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Số số hạng của tổng:
60 - 41 + 1 = 20
Ta có:
1/41 + 1/42 + 1/43 + ... + 1/60 > 1/60 + 1/60 + 1/60 + ... + 1/60 (20 số 1/60)
= 20/60
= 1/3
Vậy 1/41 + 1/42 + 1/43 + ... + 1/60 > 1/3
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(72^{45}-72^{44}=72^{44}.\left(72-1\right)=72^{44}.71\)
\(72^{44}-72^{43}=72^{43}.\left(72-1\right)=72^{43}.71\)
Vì \(72^{44}>72^{41}\Rightarrow72^{44}.71>72^{43}.71\Rightarrow72^{45}-72^{44}>72^{44}-72^{43}\)
Theo đề bài ta có:
7245 - 7244 = 7244 x ( 72 - 1 ) = 7244 x 71
7244 - 7243 = 7243 x ( 72 - 1 ) = 7243 x 71
Mà 7244 > 7243 ; 71 = 71
=> 7245 - 7244 > 7244 - 7243
\(4^{44}=4^{11.4}=4^{11^4}=4194304^4>44^4\Rightarrow4^{44}>44^4\)
nha...
4^44 = (4^11)^4 = 4194304^4
vì 4194304 > 44
=> 4^44 > 44^4
úm ba la xin tích