Lambda

The following is a proposition based on infinite series based on Ramanujan’s Series Of:

1+2+3+4+5+6+7+………..= -1/12 _(i)

But I am getting It wrong somewhere . could anyone please me find out my mistake ?

Here it goes ::

S=1²+2²+3²+4²+5²+6²+……………………. Upto infinity

S=1+4+9+16+25+36+49+64+81+100+……………

S=1+(2+2)+(3+6)+(4+12)+(5+20)+(6+30)+(7+42)+(8+56)+(9+72)+(10+90)+………….

S=(1+2+3+4+5+………..) + (2+6+12+20+30+42+……)

From (i)

S=-1/12+2x(1+3+6+10+15+21+………………)

S+1/12=2x(1+3+6+10+15+21+………..) _(ii)

S+1/12=2x(1+(2+1)+(3+3)+(4+6)+(5+10)+……..)

S+1/12=2x{(1+2+3+4………..) + (1+3+6+10+15+…….)}

S+1/12=2x (1+3+6+10+15+…….)+(-1/6)

From (ii)

S+1/12=S+1/12+(-1/6)

-1=6

So Can anyone point it where I am wrong ??