32+54+98+1716+…+257256.-数学

题目简介

32+54+98+1716+…+257256.-数学

题目详情

3
2
+
5
4
+
9
8
+
17
16
+…+
257
256
题型:解答题难度:中档来源:不详

答案

class="stub"3
2
+class="stub"5
4
+class="stub"9
8
+class="stub"17
16
+…+class="stub"257
256

=1+class="stub"1
2
+1+class="stub"1
4
+1+class="stub"1
8
+1+class="stub"1
16
+…+1+class="stub"1
256

=(1+1+1+1+…+1)+(class="stub"1
2
+class="stub"1
4
+class="stub"1
8
+class="stub"1
16
+…+class="stub"1
256
),
=8+(1-class="stub"1
2
+class="stub"1
2
-class="stub"1
4
+class="stub"1
4
-class="stub"1
8
+class="stub"1
8
-class="stub"1
16
+…+class="stub"1
128
-class="stub"1
256
),
=8+(1-class="stub"1
256
),
=8+class="stub"255
256

=8class="stub"255
256

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