DisMat Bonus

bonus-0.pdf

Show that any nonnegative integer $t$, we have the identity

$$\left(\genfrac{}{}{0ex}{}{8t}{0}\right)-\left(\genfrac{}{}{0ex}{}{8t}{2}\right)+\left(\genfrac{}{}{0ex}{}{8t}{4}\right)-...+\left(\genfrac{}{}{0ex}{}{8t}{8t}\right)=16^t$$ $$(1+x{)}^{8t}+(1-x{)}^{8t}=2\sum _{k=0}^n\left(\genfrac{}{}{0ex}{}{8t}{k}\right)x^k$$ $$1+\left(\genfrac{}{}{0ex}{}{8t}{2}\right)+\left(\genfrac{}{}{0ex}{}{8t}{8}\right)+\left(\genfrac{}{}{0ex}{}{8t}{16}\right)+...+\left(\genfrac{}{}{0ex}{}{8t}{4t}\right)=16^t$$

B.4

Transclude of dismat-bonus-ue-04.excalidraw