In this blog post, we will be learning the trick to sum up two consecutive squares.
Let us assume the numbers to be A, B (i.e A+1).
Rule: A^2 + (A+1)^2 = 2A^2 + 2A +1
Now let us look at few examples:
Example 1: 25^2 + 26^2 = 2 × 25^2 + 2 × 25 + 1
= 2 × 625 + 51= 1301.
Example 2: 58^2 +59^2 = 2 × 58^2 + 2 × 58 + 1
= 2 × [33|64] + 117
= 6728 +117 = 6845.
Example 3: 94^2 + 95^2 = 2 × 94^2+ 2 × 94 + 1
= 2 × [88|36] + 189
= 17672 + 189 = 17861.
Example 4: 48^2 + 49^2 = 2 × 48^2 + 2 × 48 + 1
= 2 × [23|04] + 97 = 4705.
Example 5: 52^2 + 53^2 = 2 × 52^2+ 2 × 52 + 1
= 2 × [27|04] + 105 = 5513.
Solve the following by yourself:
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12^2 + 13^2 =
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97^2 + 98^2 =
Happy Learning! I hope you read the other published post where the numbers are not consecutive numbers.
“The essence of Mathematics lies in its freedom”
— Georg Cantor