giup toi vs nha N=1+3^1+3^2+…+3^99 Biet 1^2+2^2+3^2+…+10^2=385 Tinh2^2+4^2+…+20^2 Thank you

Giải thích các bước giải:

\(\begin{array}{l}
N = 1 + {3^1} + {3^2} + {3^3} + …. + {3^{99}}\\
 \Rightarrow 3N = 3 + {3^2} + {3^3} + {3^4} + …. + {3^{100}}\\
 \Rightarrow 3N – N = \left( {3 + {3^2} + {3^3} + {3^4} + …. + {3^{100}}} \right) – \left( {1 + 3 + {3^2} + {3^3} + …. + {3^{99}}} \right)\\
 \Leftrightarrow 2N = {3^{100}} – 1\\
 \Leftrightarrow N = \frac{{{3^{100}} – 1}}{2}
\end{array}\) 

Lại có:

\(\begin{array}{l}
{2^2} + {4^2} + {6^2} + …. + {20^2}\\
 = {\left( {2.1} \right)^2} + {\left( {2.2} \right)^2} + {\left( {2.3} \right)^2} + …. + {\left( {2.10} \right)^2}\\
 = {2^2}{.1^2} + {2^2}{.2^2} + {2^2}{.3^2} + …. + {2^2}{.10^2}\\
 = {2^2}.\left( {{1^2} + {2^2} + {3^2} + …. + {{10}^2}} \right)\\
 = 4.385 = 1540
\end{array}\)