Question

tính tổng

S=2+2²+2³+...+2^20

B = 3+3³+3⁵+...+3²¹

Answer 1

Giải:

a)

\(S=2+2^2+2^3+...+2^{20}\)

\(\Leftrightarrow2S=2\left(2+2^2+2^3+...+2^{20}\right)\)

\(\Leftrightarrow2S=2^2+2^3+2^4+...+2^{21}\)

\(\Leftrightarrow2S-S=2^{21}-2\)

\(\Leftrightarrow S=2^{21}-2\)

Vậy ...

b)

\(B=3+3^3+3^5+...+3^{21}\)

\(\Leftrightarrow3^2B=3^2\left(3+3^3+3^5+...+3^{21}\right)\)

\(\Leftrightarrow9B=3^3+3^5+3^7+...+3^{23}\)

\(\Leftrightarrow9B-B=3^{23}-3\)

\(\Leftrightarrow8B=3^{23}-3\)

\(\Leftrightarrow B=\dfrac{3^{23}-3}{8}\)

Vậy ...