Question

S=1+3+3²+...3^99. 

Chung minh chia hét cho 10

Answer 1

Ta có: S=1+3+3^2+3^3+...+3^99 
S = (1+3^1+3^2+3^3) + (3^5+3^6+3^7+3^8) + ... + (3^96+3^97+3^98+3^99) (cứ 4 số hạng gộp lại) 
S=(1+3^1+3^2+3^3) + 3^5(1+3^1+3^2+3^3) + ...+3^96(1+3^1+3^2+3^3) 
Mà 1+3^1+3^2+3^3 = 40 
Nên S= 40 + 3^5.40 +... + 3^96.40 
=40.(1+3^5+...+3^96)

=10.4(1+3^5+..+3^96)  ( chia hết cho 10) 

Vậy S chia hết cho 10

Answer 2

S= ( 1+3+3^2))+...+(3^98+3^99)

=3*(1+3^2)+..+3^98*(1+3^2)

=3*4+...+3^98*4

=3*4+...+3^99*3*4

=12+...+3^99*12

=S=(1+...+3^99)*10 chia het cho10 

=> S chia het cho 10

Minh nghi la vayt vi minh cung ko chac la dung neu sai thi mong ban thong cam !