In the solution below provided by this website, I don't understand how the author got "Q=37N/2(N+1)=37/2(1+1/N)" from "qi=37/2(N+1)". Can you please walk me through the reasoning?

e) If there are N firms, the profit of i-th firm, i=Pqi30qi=(37020j=1,...,Nqj)qi

Maximizing profit, di/dqi=0

ie,37020q120qi140qi20qi+120qN=0

ie,qi=[372(q1++qi1+qi+1++qN)]/4is the best response function of the i-th firm.

As the firms are identical, q1==qN

So, 4qi=372(N1)qi

ie,qi(4+2N2)=37

ie,qi=37/2(N+1)

Q=37N/2(N+1)=37/2(1+1/N)

P=400-20*37N/2(N+1)=(800N+800-740N)/2(N+1)=(800+60N)/2(N+1)=(400+30N)/(N+1)=370/(N+1)+30

As N rises 1/N falls so, Q rises and Price falls.

The consumer's surplus is=.5(400-370/(N+1)-30)*(37/2(1+1/N))=.5(370-370/(N+1))*(37/2(1+1/N))=(.5*370*37/2)(1-1/(N+1))(N/(1+N))=3422.5(1/(1+1/N))²

As N rises 1/(1+1/N) goes towards 1 and as a result the consumer surplus grows close to that of perfect competition.