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Question

# Match the following with their equivalents.

A
1+3+5+7+9+11+13
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B
12+13
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C
5×7
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D
6+10
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Solution

## Every square number n can be written as the sum of consecutive n odd natural numbers starting from 1. So, 1+3+5+7+9+11+13 = 72 = 49 For any odd number 'n', n2=n2−12+n2+12 So, for 25=52, 25=25−12+25+12=12+13 For any natural number 'n', n2−1=(n−1)(n+1) So, 62−1=(6−1)(6+1)=5(7)=35 Any square number can be written as sum of 2 consecutive triangular numbers. So, 42=16=6+10, where, 6 and 10 both are triangular numbers.

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