Jawaban: Nilai dari deret tersebut pada soal adalah 3. (opsi a)
Pembahasan
Kita akan menentukan nilai dari
Untuk setiap suku, kita kalikan dengan bentuk sekawan-sekawannya (bentuk konjugat). Kita telusuri untuk setiap suku (karena latex Brainly hanya mengizinkan maksimal 512 karakter).
Dan seterusnya, hingga
Oleh karena itu, nilai/jumlah deret tersebut adalah:
Jawaban: Nilai dari deret tersebut pada soal adalah 3. (opsi a)
Pembahasan
Kita akan menentukan nilai dari
![\begin{aligned}S&=\frac{1}{\left(\sqrt{1}+\sqrt{2}\right)\left(\sqrt[4]{1}+\sqrt[4]{2}\right)}\\&\ \:\vdots\ \ +\frac{1}{\left(\sqrt{2}+\sqrt{3}\right)\left(\sqrt[4]{2}+\sqrt[4]{3}\right)}\\&\ \:\vdots\ \ +\frac{1}{\left(\sqrt{3}+\sqrt{4}\right)\left(\sqrt[4]{4}+\sqrt[4]{5}\right)}\\&\ \:\vdots\ \ +\ \dots\\&\ \:\vdots\ \ +\frac{1}{\left(\sqrt{255}+\sqrt{256}\right)\left(\sqrt[4]{255}+\sqrt[4]{256}\right)}\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7DS%26%3D%5Cfrac%7B1%7D%7B%5Cleft%28%5Csqrt%7B1%7D%2B%5Csqrt%7B2%7D%5Cright%29%5Cleft%28%5Csqrt%5B4%5D%7B1%7D%2B%5Csqrt%5B4%5D%7B2%7D%5Cright%29%7D%5C%5C%26%5C%20%5C%3A%5Cvdots%5C%20%5C%20%2B%5Cfrac%7B1%7D%7B%5Cleft%28%5Csqrt%7B2%7D%2B%5Csqrt%7B3%7D%5Cright%29%5Cleft%28%5Csqrt%5B4%5D%7B2%7D%2B%5Csqrt%5B4%5D%7B3%7D%5Cright%29%7D%5C%5C%26%5C%20%5C%3A%5Cvdots%5C%20%5C%20%2B%5Cfrac%7B1%7D%7B%5Cleft%28%5Csqrt%7B3%7D%2B%5Csqrt%7B4%7D%5Cright%29%5Cleft%28%5Csqrt%5B4%5D%7B4%7D%2B%5Csqrt%5B4%5D%7B5%7D%5Cright%29%7D%5C%5C%26%5C%20%5C%3A%5Cvdots%5C%20%5C%20%2B%5C%20%5Cdots%5C%5C%26%5C%20%5C%3A%5Cvdots%5C%20%5C%20%2B%5Cfrac%7B1%7D%7B%5Cleft%28%5Csqrt%7B255%7D%2B%5Csqrt%7B256%7D%5Cright%29%5Cleft%28%5Csqrt%5B4%5D%7B255%7D%2B%5Csqrt%5B4%5D%7B256%7D%5Cright%29%7D%5Cend%7Baligned%7D "\begin{aligned}S&=\frac{1}{\left(\sqrt{1}+\sqrt{2}\right)\left(\sqrt[4]{1}+\sqrt[4]{2}\right)}\\&\ \:\vdots\ \ +\frac{1}{\left(\sqrt{2}+\sqrt{3}\right)\left(\sqrt[4]{2}+\sqrt[4]{3}\right)}\\&\ \:\vdots\ \ +\frac{1}{\left(\sqrt{3}+\sqrt{4}\right)\left(\sqrt[4]{4}+\sqrt[4]{5}\right)}\\&\ \:\vdots\ \ +\ \dots\\&\ \:\vdots\ \ +\frac{1}{\left(\sqrt{255}+\sqrt{256}\right)\left(\sqrt[4]{255}+\sqrt[4]{256}\right)}\end{aligned}")
Untuk setiap suku, kita kalikan dengan bentuk sekawan-sekawannya (bentuk konjugat). Kita telusuri untuk setiap suku (karena latex Brainly hanya mengizinkan maksimal 512 karakter).
Dan seterusnya, hingga
Oleh karena itu, nilai/jumlah deret tersebut adalah:
KESIMPULAN
∴ Nilai dari
![\begin{aligned}&\frac{1}{\left(\sqrt{1}+\sqrt{2}\right)\left(\sqrt[4]{1}+\sqrt[4]{2}\right)}\\&\ \:\vdots\ \ +\frac{1}{\left(\sqrt{2}+\sqrt{3}\right)\left(\sqrt[4]{2}+\sqrt[4]{3}\right)}\\&\ \:\vdots\ \ +\frac{1}{\left(\sqrt{3}+\sqrt{4}\right)\left(\sqrt[4]{4}+\sqrt[4]{5}\right)}\\&\ \:\vdots\ \ +\ \dots\\&\ \:\vdots\ \ +\frac{1}{\left(\sqrt{255}+\sqrt{256}\right)\left(\sqrt[4]{255}+\sqrt[4]{256}\right)}\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%26%5Cfrac%7B1%7D%7B%5Cleft%28%5Csqrt%7B1%7D%2B%5Csqrt%7B2%7D%5Cright%29%5Cleft%28%5Csqrt%5B4%5D%7B1%7D%2B%5Csqrt%5B4%5D%7B2%7D%5Cright%29%7D%5C%5C%26%5C%20%5C%3A%5Cvdots%5C%20%5C%20%2B%5Cfrac%7B1%7D%7B%5Cleft%28%5Csqrt%7B2%7D%2B%5Csqrt%7B3%7D%5Cright%29%5Cleft%28%5Csqrt%5B4%5D%7B2%7D%2B%5Csqrt%5B4%5D%7B3%7D%5Cright%29%7D%5C%5C%26%5C%20%5C%3A%5Cvdots%5C%20%5C%20%2B%5Cfrac%7B1%7D%7B%5Cleft%28%5Csqrt%7B3%7D%2B%5Csqrt%7B4%7D%5Cright%29%5Cleft%28%5Csqrt%5B4%5D%7B4%7D%2B%5Csqrt%5B4%5D%7B5%7D%5Cright%29%7D%5C%5C%26%5C%20%5C%3A%5Cvdots%5C%20%5C%20%2B%5C%20%5Cdots%5C%5C%26%5C%20%5C%3A%5Cvdots%5C%20%5C%20%2B%5Cfrac%7B1%7D%7B%5Cleft%28%5Csqrt%7B255%7D%2B%5Csqrt%7B256%7D%5Cright%29%5Cleft%28%5Csqrt%5B4%5D%7B255%7D%2B%5Csqrt%5B4%5D%7B256%7D%5Cright%29%7D%5Cend%7Baligned%7D "\begin{aligned}&\frac{1}{\left(\sqrt{1}+\sqrt{2}\right)\left(\sqrt[4]{1}+\sqrt[4]{2}\right)}\\&\ \:\vdots\ \ +\frac{1}{\left(\sqrt{2}+\sqrt{3}\right)\left(\sqrt[4]{2}+\sqrt[4]{3}\right)}\\&\ \:\vdots\ \ +\frac{1}{\left(\sqrt{3}+\sqrt{4}\right)\left(\sqrt[4]{4}+\sqrt[4]{5}\right)}\\&\ \:\vdots\ \ +\ \dots\\&\ \:\vdots\ \ +\frac{1}{\left(\sqrt{255}+\sqrt{256}\right)\left(\sqrt[4]{255}+\sqrt[4]{256}\right)}\end{aligned}")
adalah