Question

2square +4square+6square+...........to n terms. find the sum of this series ?

Answer 1

Hey !!!

2² + 4² + 6².......2n² is even term

hence, 4 + 8 + 36......2n²

if we taking common as 4

then , 4 ( 1² + 2² + 3²......n² )

But , as we know that ,..sum of even square no.

1² + 2² + 3²......n² = n(n + 1 ) * (2n + 6)/6

hence,

4n( n + 1 ) × ( 2n + 6 ) /6

=> 2n ( n + 1 ) ( 2n + 6) / 3 Answer ✔


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Hope it helps you !!! ..

@Rajukumar111

Answer 2

☜☆☞hey friend ☜☆☞

here is your answer ☞


_________
2² + 4² + 6².......2n² is series

then, 4 + 8 + 36......2n²

we take a common no. as 4

we get, 4 ( 1² + 2² + 3²......n² )

we know that ,..

1² + 2² + 3²......n² = [n(n + 1 )×(2n + 6)]/6

hence,

[4n( n + 1 ) × ( 2n + 6 )] /6

[ 2n ( n + 1 ) ( 2n + 6) ]/ 3 ___answer


hope it will help you