Question

find the sum of n terms of the series:5+11+19+29+41​

Answer 1

Answer:

S(n) = (n/3)•(n + 2)•(n + 4)

Solution:

Please refer to the attachments.

Note:

★ nth term of AP , a(n) or T(n) = a + (n - 1)d

Where a is the first term and d is the common difference of the AP.

★ Sum of n terms of an AP is given as ;

S(n) = (n/2)•[ 2a + (n - 1)d ]

★ S(n) = Σa(n)

★ Σc = nc , where c is any constant.

★ Σc•a(n) = c•Σa(n) , c is any constant and a(n) is nth term of any series.

★ Sum of n natural numbers is given as ;

Σn = (n/2)•(n + 1)

★ Sum of squares of n natural numbers is given as ; Σn² = (n/6)•(n + 1)•(2n + 1)

★ Sum of cubes of n natural numbers is given as ; Σn³ = [ (n/2)•(n + 1) ]²