Question

Sum of terms from k=2 to k=infinity for the expression 1/k(k-1) is?​

Answer 1

Answer:

k

=

1−

k

1

k!

k−1

=

(k−1)!

1

, for k>1

k=2

∑

100

∣(k

2

−3k+1)

(k−1)!

1

∣

=

k=2

∑

100

∣

∣

∣

∣

∣

(k−1)!

(k−1)

2

−k

∣

∣

∣

∣

∣

=

k=2

∑

100

∣

∣

∣

∣

∣

(k−2)!

k−1

−

(k−1)!

k

∣

∣

∣

∣

∣

=

∣

∣

∣

∣

∣

0!

1

−

1!

2

∣

∣

∣

∣

∣

+

∣

∣

∣

∣

∣

1!

2

−

2!

3

∣

∣

∣

∣

∣

+

∣

∣

∣

∣

∣

2!

3

−

3!

4

∣

∣

∣

∣

∣

+⋯

=

1!

2

−

0!

1

+

1!

2

−

2!

3

+

2!

3

−

3!

4

+⋯+

98!

99

−

99!

100

=1+

1!

2

−

99!

100

=3−

99!

100

Hence the value of

100!

100

2

+

k=1

∑

100

∣(k

2

−3k+1)S

k

∣

=

99!

100

+3−

99!

100

=3

Hope it helps you keep smiling :)

Answer 2

Answer:

https://doubtnut.app.link/LGy0Q0lY8ib

Step-by-step explanation:

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