1²+2²+3²+4².+25²=5525,求2²+4²+6²+8².+50²=【 】
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1²+2²+3²+4².+25²=5525,求2²+4²+6²+8².+50²=【 】
1²+2²+3²+4².+25²=5525,求
2²+4²+6²+8².+50²=【 】
1²+2²+3²+4².+25²=5525,求2²+4²+6²+8².+50²=【 】
22100,马上给你说为什么
2²+4²+6²+8².+50²
=(2×1)²+(2×2)²+(2×3)²+(2×4)²+…(2×25)²
=1²×2²+2²×2²+3²×2²+4²×2².+25²×2²
=4×(1²+2²+3²+4².+25²)
=4×5525
=22100
2²+4²+6²+8²....+50²=4(1²+2²+3²+4²....+25²)=4*5525
原式=(2×1)²+(2×2)²+....+(2×25)²
=2²×1²+2²×2²+....+2²×25²
=4×5525
=22100
2²+4²+6²+8²....+50²=(2*1)²+(2*2)²+(2*3)²+(2*4)²....+(2*25)²=4*( 1²+2²+3²+4²....+25²)=4*5525 =22100
提示2^2=(1+1)^2=1^2+1^2+2*1^2=4*1^2,明白了吧,只需把5525乘以4即可~呵呵