SOLUTION: 1.Prove that 3^n=Summation(r=0,n)2^rC(n,r) 2. Evaluate summation(n=1,20)(1.1)^n

Question 874363: 1.Prove that 3^n=Summation(r=0,n)2^rC(n,r)
2. Evaluate summation(n=1,20)(1.1)^n
Answer by Edwin McCravy(20055) (Show Source): You can put this solution on YOUR website!

The binomial theorem is

1.Prove that 3^n=Summation(r=0,n)2^rC(n,r)

Since 3 = 1+2, let x=1 and y=2 in the binomial theorem

2. Evaluate summation(n=1,20)(1.1)^n



That's the sum of a geometric series with a₁ = 1.1, r=1.1, n=20

Substitute in the sum formula for a geometric series:





Edwin

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