Question

Tính:

a)S = a + a^3 + a^5 +...+ a^2n+1,với (a>=2, n thuộc N*)

b)S₁ = 1 + a^2 + a^4 + a^6 +...+ a^2n,với (a>=2, n thuộc N)

Answer 1

\(S=a+a^3+...+a^{2n+1}\)

\(S.a^2=a^3+a^5+...+a^{2n+1}+a^{2n+3}\)

\(\Rightarrow S\left(a^2-1\right)=a^{2n+3}-a\)

\(\Rightarrow S=\dfrac{a^{2n+3}-a}{a^2-1}\)

\(S_1=1+a^2+...+a^{2n}\)

\(S_1.a^2=a^2+a^4+...+a^{2n}+a^{2n+2}\)

\(\Rightarrow S_1\left(a^2-1\right)=a^{2n+2}-1\)

\(\Rightarrow S_1=\dfrac{a^{2n+2}-1}{a^2-1}\)