The value of the expression 3(1!) - 4(2!) + 5(3!) - 6(4!) ...... … - Vidyadip

MCQ

The value of the expression
$3(1!) - 4(2!) + 5(3!) - 6(4!) ...... - 2008(2006)!+ (2007)!$ is

A
$-2007$
B
$-1$
✓
$1$
D
$2007$

✓

Answer

Correct option: C.

$1$

c
$T_1 = (2 + 1)(1!) = 2! + 1!$
$T_2 = -(3 + 1)(2!) = (3! + 2!)$
$T_3 = (4 + 1)(3!) = 4! + 3!$
:
Sum $= 1$

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