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Nataly_w [17]
3 years ago
9

Which summation formula represents the series below? 1 + 2 + 6 + 24

Mathematics
1 answer:
krek1111 [17]3 years ago
6 0

Question:

Which summation formula represents the series below? 1 + 2 + 6 + 24

(a) \sum_{n=2}^{5}(n-1) !

(b) \sum_{n=0}^{3} n !

(c) \sum_{n=1}^{4}(n+1) !

(d) \sum_{n=2}^{5} n !

Answer:

Option a: \sum_{n=2}^{5}(n-1) ! is the correct answer.

Explanation:

Option a: \sum_{n=2}^{5}(n-1) !

By substituting the values of n and expanding the summation, we have,

(2-1) !+(3-1) !+(4-1) !+(5-1) !

Subtracting, we have,

1 !+2!+3 !+4 !

Expanding the factorial,

1+(2*1)+(3*2*1)+(4*3*2*1)

Simplifying, we get,

1+2+6+24

Thus, the summation \sum_{n=2}^{5}(n-1) ! represents the series 1+2+6+24

Hence, Option a is the correct answer.

Option b: \sum_{n=0}^{3} n !

By substituting the values of n and expanding the summation, we have,

0!+1!+2!+3!

Expanding the factorial,

0+1+(2*1)+(3*2*1)

Simplifying, we get,

0+1+2+6

Thus, the summation \sum_{n=0}^{3} n ! does not represents the series 1+2+6+24

Hence, Option b is not the correct answer.

Option c: \sum_{n=1}^{4}(n+1) !

By substituting the values of n and expanding the summation, we have,

(1+1) !+(2+1) !+(3+1) !+(4+1) !

Adding, we have,

2!+3!+4!+5!

Expanding the factorial,

(2*1)+(3*2*1)+(4*3*2*1)+(5*4*3*2*1)

Simplifying, we get,

2+6+24+120

Thus, the summation \sum_{n=1}^{4}(n+1) ! does not represents the series 1+2+6+24

Hence, Option c is not the correct answer.

Option d: \sum_{n=2}^{5} n !

By substituting the values of n and expanding the summation, we have,

2!+3!+4!+5!

Expanding the factorial,

(2*1)+(3*2*1)+(4*3*2*1)+(5*4*3*2*1)

Simplifying, we get,

2+6+24+120

Thus, the summation \sum_{n=2}^{5} n ! does not represents the series 1+2+6+24

Hence, Option d is not the correct answer.

Hence, the correct answer is Option a: \sum_{n=2}^{5}(n-1) !

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