Question

http://prntscr.com/knfke0

Answer 1

Let, S=2²+4²+6²+...+(2n)².

∴S=(1*2)²+(2*2)²+(3*2)²+...+(n*2)²,

=1²*2²+2²*2²+3²*2²+...+n²*2²,

=2²{1²+2²+3²+...+n²},

=4{n/6*(n+1)(2n+1)},

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

Answer 2

@ratnakermehta20 this wann being in this style :

=4{(n/6)*(n+1)(2n+1)} ,just because the (n+1)(2n+1) are in numerator and in this way will get
=(4n/6)*(n+1)(2n+1) = (2n/3)*(n+1)(2n+1) hope in this way is more understandably

Answer 3

Thank you @ratnakermehta20 and @jhonyy9
^^^