Question

Find the 10 term of the series 1.2 + 1.7 + 2.2 +....

Answer 1

Step-by-step explanation:

1.2.4+2.3.5+3.4.6+….

∴n

th

term=n(n+1)(n+3)

∴ sum =

k=1

∑

n

k(k+1)(k+3)

=

k=1

∑

n

(k

3

+4k

2

+3k)

=

k=1

∑

n

k

3

+4

k=1

∑

n

k

2

+3

k=1

∑

n

k

[

2

n(n+1)

]

2

+

6

4n(n+1)(2n+1)

+3

2

n(n+1)

=

4

n

2

(n+1)

2

+

3

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

+

2

3

n(n+1)

=n(n+1)[

4

n(n+1)

+

3

n(2n+1)

2

3

]

=n(n+1)[

12

3n

2

+3n+16n+8+18

]

=

12

n(n+1)+(3n

2

+19n+26)