Solved: Find the mistakes in the proof fragments in 3335
Chapter 5, Problem 35(choose chapter or problem)
Theorem: For any integer n ≥ 1,
\(\sum_{i=1}^{n} i(i !)=(n+1) !-1\).
“Proof (by mathematical induction): Let the property \(\sum_{i=1}^{n} i(i !)=(n+1) !-1\).
Show that P(1) is true: When n = 1
\(\sum_{i=1}^{1} i(i !)=(1+1) !-1\)
So 1(1!) = 2! − 1
and 1 = 1
Thus P(1) is true.”
Text Transcription:
sum_i=1}^n i(i !)=(n+1) !-1
sum_{i=1}^1 i(i !)=(1+1) !-1
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