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$1^{2} + (1^{2} + 2^{2}) + (1^{2} + 2^{2} + 3^{2}) + \dots$ upto 22nd terms is

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Correct option is A

tr=12+22+…+r2=16r(r+1)(2r+1)=162r3+3r2+r∴∑r=1n tr=13⋅14n2(n+1)2+12⋅16n(n+1)(2n+1)+112n(n+1)=112n(n+1)n2+n+2n+1+1=112n(n+1)n2+3n+2=112n(n+1)2(n+2)∴∑r=122 tr=112(22)(23)2(24)=23276

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12+12+22+12+22+32+… upto 22nd terms is

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$1^{2} + (1^{2} + 2^{2}) + (1^{2} + 2^{2} + 3^{2}) + \dots$ upto 22nd terms is