Question

Find the sum of the series upto 10 terms 2,12,36,80,..?

Answer 1

Given :  2 12 36 80

To Find : Sum of series upto 10 term

Solution:

2 12 36 80

2 = 1³ + 1²

12 = 2³ + 2²

36 = 3³ + 3²

80 = 4³ + 4²

Series is  n³ + n²

∑( n³ + n²)   = ∑ n³ + ∑ n²

∑ n³  = {(n)(n + 1)/2}²

∑ n²  = n(n + 1)(2n + 1)/6

Sum of 10 term

∑( n³ + n²)   =    {(n)(n + 1)/2}² +  n(n + 1)(2n + 1)/6

n = 10

=  {(10)(10 + 1)/2}² +  10(10 + 1)(2(10) + 1)/6

=  55²  + 10(11)(21)/6

= 3025 + 385

= 3410

3410  is   sum of given series upto 10 terms

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