Дана арифметическая прогрессия 4, 6, найти сумму первых пятидесяти её членов

a1=4( первый член арифм. прогрессии), d=2(разность арифм. прогрессии),n=50

по формуле суммы n-первых членов находим:

s50=2*4+2(50-1) все поделить на 2 и умножить на 50= 2650

ответ: s50=2650

d=2

находим по формуле

s50=2*4+(50-1)*2   все это/2 и *50=2650

 

Формула sinα·cosβ=(sin(α+β)-sin(α-β))/2; sin3x·cos2x=(sin(3x+2x)-sin(3x-2x))/2=(sin5x+sinx)/2 уравнение принимает вид (sin5x+sinx)/2=sin5x; sin5x-sinx=0; или 2·sin((5x-x)/2)·cos((5x+x)/2)=0; 2sin2x·cos3x=0 sin2x=0                   или           cos3x=0 2x=πk, k∈ z           или           3x=(π/2)+πn, n∈z. x=(π/2)k,   k  ∈  z       или         x=(π/6) +(π/3)n, n  ∈ z при   k=0     х₁=0             k=1     x₂=π/2           k=2       x₃=2π/2=π           k=3     x₄=3π/2           k=4     x₅=4π/2=2π               n=0     x₆=(π/6)           n=1     x₇=(π/6)+(π/3)=π/2=  x₂           n=2     x₈=(π/6)+(2π/3)=(5π/6)           n=3     x₉=(π/6)+(3π/3)=(7π/6)           n=4     x₁₀=(π/6)+(4π/3)=(9π/6)=(3π/2)=  x₄           n=5     x₁₁=(π/6)+(5π/3)=(11π/3) о т в е т.     0;       π/2;     π;     3π/2;     2π;     π/6;   5π/6;   7π/6;   11π/6.

Panther - is a very beautiful and graceful animal. the body length reaches 91-180 cm, tail - 75-110 cm, the weight is usually 32-40 kg, but rarely exceed 100 kg. there are only in tropical countries, especially a lot of them on the island of java. black individuals may appear at parents spotted on a par with the kittens, which, as parents, have spots. but later, as it happened in java, the panthers gradually separate and interbreed only among themselves. some zoologists say that there is a probability, a complete separation from the panthers leopards in the near future that will turn them into a separate species. often, this predator lives near human settlements, held by one and goes hunting at night. it perfectly climb trees, often settling there for a day or vacation in an ambush, and sometimes even catching monkeys trees. however, in general, the panther hunts on the ground. sleeping panther on the trees, stretched out on the branches and legs dangling down. they can jump on the trees up to 5.5 meters high. there is one significant feature that distinguishes leopards from other big cats: it a habit to drag their prey into trees. therefore, their food is still intact and will not get other predators - lions and hyenas.