ai làm hộ em với ạ em sẽ tick 5 sao ạ

Đáp án:

$10)\\ a) A=2^{101}-2\\ b)B=\dfrac{5^{151}-1}{4}\\ c)C=\dfrac{3^{1001}-3}{2}.$

Giải thích các bước giải:

$10)\\ a)A=2+2^2+2^3+\dots+2^{100}\\ 2A=2^2+2^3+2^4+\dots+2^{101}\\ 2A-A=(2^2+2^3+2^4+\dots+2^{101})-(2+2^2+2^3+\dots+2^{100})\\ \Leftrightarrow A=(2^2+2^3+2^4+\dots+2^{101})-(2+2^2+2^3+\dots+2^{100})\\ \Leftrightarrow A=2^{101}-2\\ b)B=1+5+5^2+\dots+5^{150}\\ 5B=5+5^2+5^3+\dots+5^{151}\\ 5B-B=(5+5^2+5^3+\dots+5^{151})-(1+5+5^2+\dots+5^{150})\\ \Leftrightarrow 4B=5^{151}-1\\ \Leftrightarrow B=\dfrac{5^{151}-1}{4}\\ c)C=3+3^2+3^2+\dots+3^{1000}\\ 3C=3^2+3^2+3^3+\dots+3^{1001}\\ 3C-C=(3^2+3^2+3^3+\dots+3^{1001})-(3+3^2+3^2+\dots+3^{1000})\\ \Leftrightarrow 2C=3^{1001}-3\\ \Leftrightarrow C=\dfrac{3^{1001}-3}{2}.$