S = 1/2! + 2/3! + 3/4! +………….+ 2014/2015! Làm giúp mình với ạ! Mình cảm ơn 01/08/2021 Bởi Cora S = 1/2! + 2/3! + 3/4! +………….+ 2014/2015! Làm giúp mình với ạ! Mình cảm ơn
Ta có:S=1/2+2/3+3/4+...+2014/2015 S=1/2+2/3!+3/4!+…+2014/2015!S=2−1/2+3−1/3!+4−1/4!+...+2015−1/2015! S=2−1/2!+3−1/3!+4−1/4!+…+2015−1/2015!S=2/2−1/2+3/3−1/3+4/4−1/4+...+2015/201!−1/2015! S=2/2!−1/2+3/3−1/3!+4/4!−1/4!+…+2015/2015!−1/2015!S=1/1−1/+1/2−1/3+1/3−1/4+...+1/2014−1/2015 S=1/1!−1/2!+1/2!−1/3!+1/3!−1/4!+…+1/2014!−1/2015!S=1/1−1/2015 S=1/1−1/2015S=1−1/2015 Bình luận
Đáp án: $S=1-\dfrac{1}{2015!}$ Giải thích các bước giải: Ta có:$S=\dfrac{1}{2!}+\dfrac{2}{3!}+\dfrac{3}{4!}+…+\dfrac{2014}{2015!}$$\to S=\dfrac{2-1}{2!}+\dfrac{3-1}{3!}+\dfrac{4-1}{4!}+…+\dfrac{2015-1}{2015!}$$\to S=\dfrac{2}{2!}-\dfrac{1}{2!}+\dfrac{3}{3!}-\dfrac{1}{3!}+\dfrac{4}{4!}-\dfrac{1}{4!}+…+\dfrac{2015}{2015!}-\dfrac{1}{2015!}$$\to S=\dfrac{1}{1!}-\dfrac{1}{2!}+\dfrac{1}{2!}-\dfrac{1}{3!}+\dfrac{1}{3!}-\dfrac{1}{4!}+…+\dfrac{1}{2014!}-\dfrac{1}{2015!}$$\to S=\dfrac{1}{1!}-\dfrac{1}{2015!}$$\to S=1-\dfrac{1}{2015!}$ Bình luận
Ta có:
S=1/2+2/3+3/4+...+2014/2015
S=1/2+2/3!+3/4!+…+2014/2015!
S=2−1/2+3−1/3!+4−1/4!+...+2015−1/2015!
S=2−1/2!+3−1/3!+4−1/4!+…+2015−1/2015!
S=2/2−1/2+3/3−1/3+4/4−1/4+...+2015/201!−1/2015!
S=2/2!−1/2+3/3−1/3!+4/4!−1/4!+…+2015/2015!−1/2015!
S=1/1−1/+1/2−1/3+1/3−1/4+...+1/2014−1/2015
S=1/1!−1/2!+1/2!−1/3!+1/3!−1/4!+…+1/2014!−1/2015!
S=1/1−1/2015
S=1/1−1/2015
S=1−1/2015
Đáp án: $S=1-\dfrac{1}{2015!}$
Giải thích các bước giải:
Ta có:
$S=\dfrac{1}{2!}+\dfrac{2}{3!}+\dfrac{3}{4!}+…+\dfrac{2014}{2015!}$
$\to S=\dfrac{2-1}{2!}+\dfrac{3-1}{3!}+\dfrac{4-1}{4!}+…+\dfrac{2015-1}{2015!}$
$\to S=\dfrac{2}{2!}-\dfrac{1}{2!}+\dfrac{3}{3!}-\dfrac{1}{3!}+\dfrac{4}{4!}-\dfrac{1}{4!}+…+\dfrac{2015}{2015!}-\dfrac{1}{2015!}$
$\to S=\dfrac{1}{1!}-\dfrac{1}{2!}+\dfrac{1}{2!}-\dfrac{1}{3!}+\dfrac{1}{3!}-\dfrac{1}{4!}+…+\dfrac{1}{2014!}-\dfrac{1}{2015!}$
$\to S=\dfrac{1}{1!}-\dfrac{1}{2015!}$
$\to S=1-\dfrac{1}{2015!}$