Toán Lớp 7: A = 3 +3^2 +3^3 +3^4 +- +3^99+ 3^100

Question

Toán Lớp 7:  A = 3 +3^2 +3^3 +3^4 +.... +3^99+ 3^100

tuyethutanhthu · Answer

~ Bạn tham khảo ~   A = 3+3^2+3^3+3^4+...+3^99+3^100   3A = 3^2 + 3^3+3^4 +3^5+....+3^100+3^101   3A -  A = ( 3^2 + 3^4 +3^5+....+3^100+3^101)-(3+3^2+3^3+3^4+...+3^99+3^100)   3A - A = 3^101 - 3   2A = 3^101-3   A = (3^101-3)/2   Vậy  A = (3^101-3)/2   $#Vịt v&agrave;ng$

tuminh25 · Answer

$ text{ A = 3 + $3^2$ + $3^3$ + $3^4$  + ... + + $3^9$$ ^9$  + $3^1$$ ^0$$ ^0$ }$   $ Rightarrow$ $ text{ 3A = 3. ( 3 + $3^2$ + $3^3$ + $3^4$  + ... + + $3^9$$ ^9$  + $3^1$$ ^0$$ ^0$ ) }$   $ Rightarrow$ $ text{ 3A = $3^2$ + $3^3$ + $3^4$  + ... + + $3^9$$ ^9$  + $3^1$$ ^0$$ ^0$ + $3^1$$ ^0$$ ^1$ }$   $ Rightarrow$$ text{ 3A - A = ( $3^2$ + $3^3$ + $3^4$  + ... + + $3^9$$ ^9$  + $3^1$$ ^0$$ ^0$ + $3^1$$ ^0$$ ^1$ ) - ( 3 + $3^2$ + $3^3$ + $3^4$  + ... + + $3^9$$ ^9$  + $3^1$$ ^0$$ ^0$ ) }$   $ Rightarrow$ $ text{ 2A = $3^1$$ ^0$$ ^1$ - 3 }$   $ Rightarrow$ $ text{ A = ( $3^1$$ ^0$$ ^1$ - 3 ) : 2 }$       $ text{ Vậy A = $ dfrac{3^101 - 3}{2}$ }$