Question

find the sum of n terms. 1³ + (1³+2³)/2 +(1³+2³+3³)/3 +.....​

Answer 1

Answer:

Step-by-step explanation:

Tn = (13 + 23 + 33 + ………)/(1 + 3 + 5 ……..)

n times = {n2(n + 1)2/4}/{(n/2)(2 + 2n – 2)}

So, Tn = {n2(n + 1)2/4}/(n2) Tn = (n + 1)2/4

So, Sn = (1/4) [ n(n + 1)(2n + 1)/6 + n + 2n(n + 1)/2 ]

Sn = (n/4) [ (n + 1)(2n + 1)/6 + 1 + (n + 1) ]

Sn = (n/24) [ (2n2 + 3n + 1) + 6n + 12 ]

Sn = (n/24) [ 2n2 + 9n + 13 ]