利用因式分解计算1-2²+3²-4²+5²-6²+.+99²-100²+101²
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![利用因式分解计算1-2²+3²-4²+5²-6²+.+99²-100²+101²](/uploads/image/z/241033-49-3.jpg?t=%E5%88%A9%E7%94%A8%E5%9B%A0%E5%BC%8F%E5%88%86%E8%A7%A3%E8%AE%A1%E7%AE%971-2%26%23178%3B%2B3%26%23178%3B-4%26%23178%3B%2B5%26%23178%3B-6%26%23178%3B%2B.%2B99%26%23178%3B-100%26%23178%3B%2B101%26%23178%3B)
利用因式分解计算1-2²+3²-4²+5²-6²+.+99²-100²+101²
利用因式分解计算1-2²+3²-4²+5²-6²+.+99²-100²+101²
利用因式分解计算1-2²+3²-4²+5²-6²+.+99²-100²+101²
1-2²+3²-4²+5²-6²+.+99²-100²+101²
=1+3²-2²+5²-4²+7²-6²+.+99²-98²+101²-100²
=1+(3+2)(3-2)+(5+4)(5-4)+.+(101+100)(101-100)
=1+5+9+...+201
=(1+201)*51÷2
=101*51
=5151
1 - 2" + 3" - 4" + 5" - 6" + …… + 99" - 100" + 101"
= 1 + 3" - 2" + 5" - 4" + …… + 99" - 98" + 101" - 100"
= 1 + ( 3" - 2" ) + ( 5" - 4" ) + …… + ( 99" - 98" ) + ( 101" - 100" )
= 1 + ( 3 ...
全部展开
1 - 2" + 3" - 4" + 5" - 6" + …… + 99" - 100" + 101"
= 1 + 3" - 2" + 5" - 4" + …… + 99" - 98" + 101" - 100"
= 1 + ( 3" - 2" ) + ( 5" - 4" ) + …… + ( 99" - 98" ) + ( 101" - 100" )
= 1 + ( 3 - 2 )( 3 + 2 ) + ( 5 - 4 )( 5 + 4 ) + …… + ( 101 - 100 )( 101 + 100 )
= 1 + 5 + 9 + …… + 201
接下来
= 1 + ( 1X4 + 1 ) + ( 2X4 + 1 ) + …… + ( 50X4 + 1 )
= 51 + 4X1 + 4X2 + …… + 4X50
= 51 + 4 X ( 1 + 2 + …… + 50 )
= 51 + 4 X ( 50 + 1 ) X 50 / 2
继续
= 51 + 2 X 51 X 50
= 51 + 51 X 100
= 51 + 5100
= 5151
收起