Processing math: 100%


BinomialExpansion Basic
2016


Problem - 3978

Given P(x)=(1+x+x2)100=a0+a1x++a200x200

Compute the following sums:

  • S1=a0+a1+a2+a3++a200
  • S2=a0+a2+a4+a6++a200.

Setting x=1 gives the result for S1: S1=a0+a1+a2++a200=3100

Next, setting x=1 yields S1=a0a1+a2++a200=1100=1

Now, we have S2=12(S1+S1)=3100+12

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