<s>[INST] Finit Sum $\sum\limits_{i=1}^{100}i^8-2 i^2$ Can anyone help me?
How can I find 
$$\sum_{i=1}^{100}i^8-2i^2 $$
 [/INST] Hint: Expand following formula for $k=2,5,8$
$$\sum_{i=1}^n i^k=\frac{(n+1+B)^{k+1}-B^{k+1}}{k+1}$$
$$B^0=1,B^1=\frac{-1}{2},B^2=\frac{1}{6},B^3=0,B^4=\frac{-1}{30},B^5=0,B^6=\frac{1}{42},B^7=0,B^8=\frac{-1}{30},B^9=0,....$$
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