Mathematics
Let us look at the triangular numbers figure again. Add two consecutive triangular numbers. For example, T1 + T2 = 4, T2 + T3 = 9, T3 + T4 = 16.
What about T4 + T5 ? Make a conjecture about Tn-1 + Tn.
Mathematics Proofs
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Answer
Given,
⇒ T1 + T2 = 4 = 22
⇒ T2 + T3 = 9 = 32
⇒ T3 + T4 = 16 = 42
Conjecture :
On adding two triangular numbers the resultant value is the square of the larger number.
By using conjecture :
⇒ T4 + T5 = 52 = 25.
Hence, Tn - 1 + Tn = n2.
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