Дана прогрессия:
![A_n=2n-1](https://tex.z-dn.net/?f=A_n%3D2n-1)
Формула суммы первых членов
![S_n= \frac{a_1+a_n}{2}*n](https://tex.z-dn.net/?f=S_n%3D+%5Cfrac%7Ba_1%2Ba_n%7D%7B2%7D%2An)
Найдем 1 член, и n - ый член:
![A_1=2-1=1](https://tex.z-dn.net/?f=A_1%3D2-1%3D1)
![A_n=2n-1](https://tex.z-dn.net/?f=A_n%3D2n-1)
Откуда:
![S_n= \frac{n(1+2n-1)}{2}= \frac{2n^2}{2}=n^2](https://tex.z-dn.net/?f=S_n%3D+%5Cfrac%7Bn%281%2B2n-1%29%7D%7B2%7D%3D+%5Cfrac%7B2n%5E2%7D%7B2%7D%3Dn%5E2)
( a^1/4)^2 -(b^1/4)^2=
a^1/2-b^1/2
Это первые две скобочки сделали по формуле
а^2 -b^2= (a-b)(a+b)
и учитывая, что степень возводится в степень показатели перемножаются.
(а^1/2 -b^1/2)(a^1/2+b^1/2)=
(a^1/2)^2 -(b^1/2)^2=
=a-b
69 надо вроде на 76 умножать, но лучше подумай
![y(x)= \sqrt{2+sin^4(x)-cos(2x)} +\sqrt{2+cos^4(x)+cos(2x)} =\\ = \sqrt{2+(sin^2(x))^2-(1-2sin^2(x))} +\\+\sqrt{2+(cos^2(x))^2+(1-2sin^2(x))} =\\ = \sqrt{2+(sin^2(x))^2-1+2sin^2(x)} +\\+\sqrt{2+(1-sin^2(x))^2+1-2sin^2(x)} =\\ = \sqrt{1^2+2*1*sin^2(x)+(sin^2(x))^2} +\\+\sqrt{2+1-2sin^2(x)+sin^4(x)+1-2sin^2(x)} =\\ = \sqrt{(1+sin^2(x))^2} +\sqrt{2^2-2*2*sin^2(x)+(sin^2(x))^2} =\\ =\|1+sin^2(x)| +|2-sin^2(x)|=1+sin^2(x) +2-sin^2(x)=\\ =3](https://tex.z-dn.net/?f=y%28x%29%3D+%5Csqrt%7B2%2Bsin%5E4%28x%29-cos%282x%29%7D+%2B%5Csqrt%7B2%2Bcos%5E4%28x%29%2Bcos%282x%29%7D+%3D%5C%5C+%3D+%5Csqrt%7B2%2B%28sin%5E2%28x%29%29%5E2-%281-2sin%5E2%28x%29%29%7D+%2B%5C%5C%2B%5Csqrt%7B2%2B%28cos%5E2%28x%29%29%5E2%2B%281-2sin%5E2%28x%29%29%7D+%3D%5C%5C+%3D+%5Csqrt%7B2%2B%28sin%5E2%28x%29%29%5E2-1%2B2sin%5E2%28x%29%7D+%2B%5C%5C%2B%5Csqrt%7B2%2B%281-sin%5E2%28x%29%29%5E2%2B1-2sin%5E2%28x%29%7D+%3D%5C%5C+%3D+%5Csqrt%7B1%5E2%2B2%2A1%2Asin%5E2%28x%29%2B%28sin%5E2%28x%29%29%5E2%7D+%2B%5C%5C%2B%5Csqrt%7B2%2B1-2sin%5E2%28x%29%2Bsin%5E4%28x%29%2B1-2sin%5E2%28x%29%7D+%3D%5C%5C+%3D+%5Csqrt%7B%281%2Bsin%5E2%28x%29%29%5E2%7D+%2B%5Csqrt%7B2%5E2-2%2A2%2Asin%5E2%28x%29%2B%28sin%5E2%28x%29%29%5E2%7D+%3D%5C%5C+%3D%5C%7C1%2Bsin%5E2%28x%29%7C+%2B%7C2-sin%5E2%28x%29%7C%3D1%2Bsin%5E2%28x%29+%2B2-sin%5E2%28x%29%3D%5C%5C+%3D3)
Итого, графиком этой функции есть паралельная оси ОХ линия на высоте
![3](https://tex.z-dn.net/?f=3)
над ней: