Mathematics
Go back to Pascal’s triangle.
Line 1 : 1 = 110
Line 2 : 1 1 = 111
Line 3 : 1 2 1 = 112
Make a conjecture about Line 4 and Line 5. Does your conjecture hold? Does your conjecture hold for Line 6 too?
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Answer
Given,
Line 1 : 1 = 110
Line 2 : 1 1 = 111
Line 3 : 1 2 1 = 112
Looking at the above pascal triangle,
Possible conjecture :
Line 4
1 3 3 1 = 113
Line 5
1 4 6 4 1 = 114
Since, The conjecture holds for line 4 and line 5.
Line 6 :
161051 = 115
The conjecture does not holds for above line.
Hence, conjecture holds for line 4 and 5 but does not holds for line 6.
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