Question

CHO TỔNG S =4+ 3^2 +3^3 +....+3^223 .Chứng minh rằng S chia hết cho 41 ?

Answer 1

Ta co: 3+3^3+3^5+...+3^1991 = (3+3^3+3^5)+...+(3^1987+1989+1991) =3.(1+3^2+3^4)+...+3^1987.(1+3^2+3^4) =3.91+...+3^1987.91 =(3+..+3^1987).91=(3+...+3^1987).13.7 chia het cho 13 3+3^3+3^5+...+3^1991 =(3+3^3+3^5+3^7)+...+(3^1985+3^1987+3^1989+3^1991) =3(1+3^2+3^4+3^6)+...+3^1985.(1+3^2+3^4+3^6) =3.820+...+3^1985.820=(3+...+3^1985).820=(3+....+3^1985).41.20 chia het cho 41

Answer 2

WHY CHO 3^223 CƠ MÀ

Answer 3

S=4+3²+3³+...+3²²³

S=1+3+3²+3³+...+3²²³

S=(1+3⁴)+(3+3⁵)+(3²+3⁶)+(3³+3⁷)+...+(3¹¹⁹+3²²³)

S=82+3(1+3⁴)+3²(1+3⁴)+3³(1+3⁴)+...+3¹¹⁹(1+3⁴)

S=82+3.82+3².82+3³.82+...+3¹¹⁹.(1+3⁴)

S=82(3+3²+3³+...+3¹¹⁹)

vì 82⋮41⇒S⋮41

Vậy S⋮41