Question

Sa se aduca la o forma mai simpla:
S2=$C_{n} ^0 + 4 C_{n} ^2+ 4^{2} C_{n} ^4+ 4^{3} C_{n} ^6+.......$

Answer 1

Salut,

$(1+2)^n=C_n^0+2C_n^1+4C_n^2+2^3C_n^3+4^2C_n^4+2^5C_n^5+4^3C_n^6+\ldots;\\\\(1-2)^n=C_n^0-2C_n^1+4C_n^2-2^3C_n^3+4^2C_n^4-2^5C_n^5+4^3C_n^6-\ldots.$

Dacă aduni identităţile de mai sus membru cu membru, obţii că:

$S_2=\dfrac{3^n+(-1)^n}2.$

Green eyes.