Question

what is the value of this infinite series?​

Answer 1

Answer:

S=

6

5e

−

2

1

is the correct answer

Answer 2

Answer:

T

n

=

6(n+1)!

n(n+1)(2n+1)

S=∑

i=2

∞

6(n+1)!

n(n+1)(2n+1)

=∑

i=2

∞

6(n−1)!

(2n+1)

S=∑

i=2

∞

6(n−1)!

2n−2+3

S=

6

1

∑

i=2

∞

(n−1)!

2(n−1)

+

6

3

∑

i=2

∞

(n−1)!

1

S=

6

2

∑

i=2

∞

(n−2)!

1

+

2

1

∑

i=2

∞

(n−1)!

1

S=

3

1

e+

2

1

(e−1)

S=

6

5e

−

2

1