Question
Sum the series $1^{2}+2^{2}+3^{2}+\cdots+n^{2}$ by observing that$$m^{2}=2\left(\begin{array}{c}m \\2\end{array}\right)+\left(\begin{array}{c}m \\1\end{array}\right)$$and using the identity (5.19).
Step 1
The given series is $S = 1^2 + 2^2 + 3^2 + \cdots + n^2$. The given identity is $m^2 = 2\binom{m}{2} + \binom{m}{1}$. Show more…
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