Question

find the sum of the following series. 2² +4² +6² + ... + 40²​

Answer 1

Answer:

11480

Step-by-step explanation:

2²+4²+6²+...........+(2n)² =

= 2²+2²*2²+2²*3²+.......+2²*n² =

= 2²(1²+2²+3²+........+n²) =

= 2²(1/6)n (n+1) (2n+1) =

= (2/3)n (n+1) (2n+1)

for n=20, we have =2/3*20*21*41=11480