Tính tổng S = 1/2017 (2.3C 2017 2 + 3.3^2 C 2017 3 + 4.3^3 C 2017 4 +...

45/50

Tính tổng S=120172.3C20172+3.32C20173+4.33C20174+...+k.3k−1C2017k+...+2017.32016C20172017.

42016−1.

32016−1.

32016.

42016.

Giải thích

Đáp án A

(1+x)2017=C20170+C20171x+...+C20172017x2017

Lấy đạo hàm hai vế ta được:

20171+x2016 =C20171+2C20172x+...+2017C20172017x2016(1+x)2016=12017(C20171+2C20172x+...+2017C20172017x2016)x=3⇒42016=1+12017(2.3C20172+...+2017.32016C20172017)⇒12017(2.3C20172+...+2017.32016C20172017)=42016−1