The sum of 1-1- - 2-2- - - - 50-50- equals

Explanation for the correct option:Given, 1× 1!+2× 2!+...........+50× 50!,=(2 1)(1)!+(3 1)2!+(4 1)3!........+(50+1 1)50!0ex0ex=2× 1! 1+3× 2! 2!+4× 3! 3!+....... ...

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Byju's Answer

Standard VI

Mathematics

Word Problems based on Operations on Integers

The sum of 1×...

Question

The sum of $1 \times 1! + 2 \times 2! + . . . . . . . . . . . + 50 \times 50!$ equals

$51!$

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$51! - 1$

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$51! + 1$

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$2 \times 51!$

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Solution

The correct option is B
$51! - 1$

Explanation for the correct option:
Given, $1 \times 1! + 2 \times 2! + . . . . . . . . . . . + 50 \times 50!$ ,
$= (2 - 1) (1)! + (3 - 1) 2! + (4 - 1) 3! . . . . . . . . + (50 + 1 - 1) 50! = 2 \times 1! - 1 + 3 \times 2! - 2! + 4 \times 3! - 3! + . . . . . . . . . + (51) 50! - (1) 50! = 2! - 1! + 3! - 2! + . . . . . (51)! - 50! = 51! - 1$
$1 \times 1! + 2 \times 2! + . . . + 50 \times 50! = 51! - 1$
Hence, option B is correct.

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The sum of 1×1!+2×2!+...........+50×50! equals

The correct option is B 51!-1Explanation for the correct option:Given, 1×1!+2×2!+...........+50×50!,=(2-1)(1)!+(3-1)2!+(4-1)3!........+(50+1-1)50!=2×1!-1+3×2!-2!+4×3!-3!+.........+(51)50!-(1)50!=2!-1!+3!-2!+.....51!-50!=51!-11×1!+2×2!+...+50×50!=51!-1Hence, option B is correct.

The sum of $1 \times 1! + 2 \times 2! + . . . . . . . . . . . + 50 \times 50!$ equals