Question

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Answer 1

Bài 2:

$S=6^2+6^4+6^6+...+6^{98}+6^{100}$

$6^2S=6^4+6^6+6^8+...+6^{100}+6^{102}$

$\Rightarrow 6^2S-S=6^{102}-6^2$

$\Rightarrow 35S=6^{102}-36$

$\Rightarrow S=\frac{6^{102}-36}{35}$

Answer 2

Bài 3:

$S=1+3^2+3^4+...+3^{100}+3^{102}$

$3^2S=3^2+3^4+3^6+...+3^{102}+3^{104}$

$\Rightarrow 3^2S-S=3^{104}-1$
$\Rightarrow S=\frac{3^{104}-1}{8}$

Answer 3

Bài 4:

$S=1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^4}+...+\frac{1}{2^{98}}+\frac{1}{2^{100}}$

$2^2S=4+2+1+\frac{1}{2^2}+...+\frac{1}{2^{96}}+\frac{1}{2^{98}}$

$\Rightarrow 2^2S-S=4+2-\frac{1}{2}-\frac{1}{2^{100}}$

$\RIghtarrow 3S=\frac{11}{2}-\frac{1}{2^{100}}$

$\Rightarrow S=\frac{11}{6}-\frac{1}{3.2^{100}}$

Answer 4

Bài 5:

$S=\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^4}+...+\frac{1}{3^{98}}+\frac{1}{3^{100}}$

$3^2S=3+1+\frac{1}{3^2}+...+\frac{1}{3^{96}}+\frac{1}{3^{98}}$

$\Rightarrow 3^2S-S=3+1-\frac{1}{3}-\frac{1}{3^{100}}$

$\Rightarrow 8S=\frac{11}{3}-\frac{1}{3^{100}}$

$\Rightarrow S=\frac{11}{24}-\frac{1}{8.3^{100}}$