Question

りりちゃん

数学的帰納法です。ここの計算過程が分かりません！詳しく教えてください！！

(II)n=kのとき, ① が成り立つと仮定すると、
=
1
2!
=
2 3
+ +
3! 4!
n=k+1 のとき,②より,
(左辺)
1 2 3
+ + +
2! 3! 4!
(k+1)! -1
(k+1)!
+
·+··
(k+2)!-1
(k+2)!
+
(右辺)=
k
(k+1)!-1
(k+1)! (k+1)!
+
{(k+1)!-1}(k+2) k+1
(k+1)! (k+2) (k+2)!
②
k+1
(k+2)!
k
(k+1)!
+
{(k+1)!-1}(k+2)+(k+1)
(k+2)!
(k+2)! (k+2)+(k+1)
(k+2)!
【
{(k+1)+1}!
1
+
k+1
{(k+1)+1}!
三立
{(k+1)+1}!-1_(k+2)!-1
(-47-(2)
RAA
(k+2)!
(2)
jeu