tính tổng S=1+3+3^2+3^3+...+3^10
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B
3 tháng 1 2023
\(S=3^1+3^2+3^3+.....+3^{100}\) \(=\left(3^1+3^2+3^3+3^4\right)+\left(3^5+3^6+3^7+3^8\right)+...+\left(3^{97}+3^{98}+3^{99}+3^{100}\right)\)
\(=120+3^5.\left(3^1+3^2+3^3+3^4\right)+....+3^{97}.\left(3^1+3^2+3^3+3^4\right)\)
\(=1.120+3^5.120+...+3^{97}.120\)
\(=\left(1+3^5+...+3^{97}\right).120\)
\(\Rightarrow S⋮120\)
Vậy ........
9 tháng 5 2021
In modern times, our continued advance in technology has led to the explosion of many useful electronic devices, one of which is mobile phone. It has become a vital part of people’s life on account of the huge benefits it brings. To begin with, mobile phone is a source of information. With Internet access available anywhere and at any time, users can search for the latest news and keep themselves informed of events around the world. Not only providing information, it also acts as a useful device for storage. Photos, videos, records or texts can all be stored in your phone. For instance, when you attend a lecture but seem to be not quick enough to take note everything, it is possible to record it and play back several times. More than that, the important function making it increasingly appealing nowadays is a source of entertainment, offering people with a wide range of activities in the free time such as playing games, listening to music or reading e-books. Last but not least, mobile phone has been upgraded to become a multifunctional device, which can come in handy in different situations. Many cell phones often come with a GPS and a Map application, allowing users to identify their location and get the right way to the place they want. To sum up, mobile phone is undoubtedly one of the greatest inventions, which not only meet the demand for communication, information exchange and entertainment but also offers numerous useful functions that make our life easier.
PA
12 tháng 5 2016
\(\left(1-\frac{1}{2}\right)\times\left(1-\frac{1}{3}\right)\times\left(1-\frac{1}{4}\right)\times.....\times\left(1-\frac{1}{99}\right)\times\left(1-\frac{1}{100}\right)\)
\(=\frac{1}{2}\times\frac{2}{3}\times\frac{3}{4}\times.....\times\frac{98}{99}\times\frac{99}{100}\)
\(=\frac{1}{100}\)
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S=1+3+3^2+3^3+...+3^10
3.S=3+3^2+3^3+3^4+...+3^11
3.S-S=(3+3^2+3^3+3^4+...+3^10)-(1+3+3^2+3^3+...+3^10
3.S-S=3+3^2+3^3+3^4+...+3^11-1-3-3^2-3^3-...-3^10
S=3^11-1