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Question Number 194135 by cortano12 last updated on 28/Jun/23
23!−231.1!+2.2!+3.3!+...+21.21!=?
Answered by Frix last updated on 28/Jun/23
23[∑nj=1j×j!=(n+1)!−1]
Answered by aba last updated on 28/Jun/23
1.1!+2.2!+...+21.21!=(2−1)1!+(3−1)2!+...+(22−1)21!=2!−1!+3!−2!+...+22!−21!=22!−1!A=23!−231.1!+2.2!+...+21.21!=23(22!−1)22!−1!=23✓
Answered by MM42 last updated on 28/Jun/23
n×n!=(n+1)!−n!⇒s=1×1!+2×2!+3×3!+...+21×22!=(2!−1!)+(3!−2!)+(4!−3!)+...+(21!−20!)+(22!−21!)=22!−1⇒23!−23s=23(22!−1)22!−1=23✓
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