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Adding Triangular Numbers

Find the 14 -...

Question

Find the 14-th and 15-th triangular numbers, and find their sum. Verify the Statement 8 for this sum.

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Solution

The 14^th and 15^th triangular numbers are:

14^th triangular number = 1 + 2 + 3 + 4 + … + 14 = 105

15^th triangular number = 1 + 2 + 3 + 4 + … + 14 + 15 = 120

Sum of the 14^th and 15^th triangular numbers = (14 + 1)² = 225

Here, 105 + 120 = 225

Hence, statement 8 is verified.

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