Question
The sum of first $n$ terms of the series$1 \cdot 1 !+2 \cdot 2 !+3 \cdot 3 !+4 \cdot 4 !+\ldots$ is(A) $(n+1) !-1$(B) $n !-1$(C) $(n-1) !-1$(D) None of these
Step 1
Step 1: We can rewrite each term in the series as follows: $1 \cdot 1 ! = (2-1) \cdot 1 !$ $2 \cdot 2 ! = (3-1) \cdot 2 !$ $3 \cdot 3 ! = (4-1) \cdot 3 !$ $\vdots$ $n \cdot n ! = (n+1-1) \cdot n !$ Show more…
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