Следующее число которое одинаково читается в обоих направлениях: 13031
Тогда:
13031-12921=110
тогда 110/2 = 55 км/ч - ехал автомобиль
1) а10=а1+9*д
-46=-1+9д
-9д=-1+46
-9д=45
д=-5
-86=-1(-5*n-1)
5*n-1=-1+86
5*n-1=85
n-1=17
n=18
ответ:да,являеться
2)а7=а1+6д
-9=3+6д
-6д=3+9
-6д=12
д=-2
-35=3+(-2*n-1)
-2*n-1=3+35
n-1=38/-2
n-1=-19
n=-18
ответ:да, являеться
27a^2 - 18ab=3a*9a-2b*9a=9a(3a-2b)
1) Пусть n=2
![1+ \frac{1}{ \sqrt{2} } \ \textgreater \ \sqrt{2} \\ \\ \sqrt{2}* (1+ \frac{1}{ \sqrt{2} } ) \ \textgreater \ \sqrt{2} *\sqrt{2} \\ \\ \sqrt{2} +1\ \textgreater \ 2 \\ \\ \sqrt{2} \ \textgreater \ 1 \\ \\](https://tex.z-dn.net/?f=1%2B+%5Cfrac%7B1%7D%7B+%5Csqrt%7B2%7D+%7D++%5C+%5Ctextgreater+%5C++%5Csqrt%7B2%7D++%5C%5C++%5C%5C++%5Csqrt%7B2%7D%2A+%281%2B+%5Cfrac%7B1%7D%7B+%5Csqrt%7B2%7D+%7D+%29+%5C+%5Ctextgreater+%5C+++%5Csqrt%7B2%7D+%2A%5Csqrt%7B2%7D++%5C%5C++%5C%5C++%5Csqrt%7B2%7D+%2B1%5C+%5Ctextgreater+%5C+2+%5C%5C++%5C%5C+%5Csqrt%7B2%7D+%5C+%5Ctextgreater+%5C+1+%5C%5C++%5C%5C)
верно
2)Пусть верно при n=k
![1+ \frac{1}{ \sqrt{2} } + \frac{1}{ \sqrt{3} } +...+ \frac{1}{ \sqrt{k} } \ \textgreater \ \sqrt{k} \\ \\](https://tex.z-dn.net/?f=1%2B+%5Cfrac%7B1%7D%7B+%5Csqrt%7B2%7D+%7D+%2B+%5Cfrac%7B1%7D%7B+%5Csqrt%7B3%7D+%7D+%2B...%2B+%5Cfrac%7B1%7D%7B+%5Csqrt%7Bk%7D+%7D+%5C+%5Ctextgreater+%5C++%5Csqrt%7Bk%7D++%5C%5C++%5C%5C+)
3)докажем, что верно при n=k+1
![1+ \frac{1}{ \sqrt{2} } + \frac{1}{ \sqrt{3} } +...+ \frac{1}{ \sqrt{k} } + \frac{1}{ \sqrt{k+1} } \ \textgreater \ \sqrt{k}+ \frac{1}{ \sqrt{k+1} } \\ \\](https://tex.z-dn.net/?f=1%2B+%5Cfrac%7B1%7D%7B+%5Csqrt%7B2%7D+%7D+%2B+%5Cfrac%7B1%7D%7B+%5Csqrt%7B3%7D+%7D+%2B...%2B+%5Cfrac%7B1%7D%7B+%5Csqrt%7Bk%7D+%7D+%2B+%5Cfrac%7B1%7D%7B+%5Csqrt%7Bk%2B1%7D+%7D+%5C+%5Ctextgreater+%5C+%5Csqrt%7Bk%7D%2B+%5Cfrac%7B1%7D%7B+%5Csqrt%7Bk%2B1%7D+%7D++%5C%5C++%5C%5C+)
![\frac{1}{ \sqrt{k+1} } -](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B+%5Csqrt%7Bk%2B1%7D+%7D+-+)
положительное число
![\sqrt{k} + \frac{1}{ \sqrt{k+1} } \ \textgreater \ \sqrt{k+1} \\ \\ \sqrt{k+1}*( \sqrt{k} + \frac{1}{ \sqrt{k+1} } )\ \textgreater \ \sqrt{k+1} * \sqrt{k+1} \\ \\ \sqrt{k(k+1)} +1\ \textgreater \ k+1 \\ \\ \sqrt{k^2+k} \ \textgreater \ \sqrt{k^2} ;k \geq 2 \\ \\](https://tex.z-dn.net/?f=+%5Csqrt%7Bk%7D+%2B+%5Cfrac%7B1%7D%7B+%5Csqrt%7Bk%2B1%7D+%7D+%5C+%5Ctextgreater+%5C++%5Csqrt%7Bk%2B1%7D++%5C%5C++%5C%5C+%5Csqrt%7Bk%2B1%7D%2A%28+%5Csqrt%7Bk%7D+%2B+%5Cfrac%7B1%7D%7B+%5Csqrt%7Bk%2B1%7D+%7D+%29%5C+%5Ctextgreater+%5C++%5Csqrt%7Bk%2B1%7D+%2A+%5Csqrt%7Bk%2B1%7D++%5C%5C++%5C%5C++%5Csqrt%7Bk%28k%2B1%29%7D+%2B1%5C+%5Ctextgreater+%5C+k%2B1+%5C%5C++%5C%5C++%5Csqrt%7Bk%5E2%2Bk%7D+%5C+%5Ctextgreater+%5C++%5Csqrt%7Bk%5E2%7D+%3Bk+%5Cgeq+2+%5C%5C++%5C%5C+)
верно
⇒
![1+ \frac{1}{ \sqrt{2} } + \frac{1}{ \sqrt{3} } +...+ \frac{1}{ \sqrt{k} } + \frac{1}{ \sqrt{k+1} } \ \textgreater \ \sqrt{k+1} } \\ \\](https://tex.z-dn.net/?f=1%2B+%5Cfrac%7B1%7D%7B+%5Csqrt%7B2%7D+%7D+%2B+%5Cfrac%7B1%7D%7B+%5Csqrt%7B3%7D+%7D+%2B...%2B+%5Cfrac%7B1%7D%7B+%5Csqrt%7Bk%7D+%7D+%2B+%5Cfrac%7B1%7D%7B+%5Csqrt%7Bk%2B1%7D+%7D+%5C+%5Ctextgreater+%5C+%5Csqrt%7Bk%2B1%7D+%7D+%5C%5C+%5C%5C+)
ч.т.д.