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Chapter 12: Q 58. (page 809)

In Problems 51鈥�60, write out each sum.

鈭�k=0n-12k+1

Short Answer

Expert verified

The required sum is鈭�k=0n-12k+1=1+3+5+.......+2n-1.

Step by step solution

01

Step 1. Write the given information.

The given summation notation is:

鈭�k=0n-12k+1

02

Step 2. Write out the sum.

To get the sum, we need to substitute 0,1,2,.......,n-1for k,in the given sequence 鈭�k=0n-12k+1,

鈭�k=0n-12k+1=2路0+1+2路1+1+2路2+1+.......+2路n-1+1=0+1+2+1+4+1+.......+2n-2+1=1+3+5+.......+2n-1

Therefore,鈭�k=0n-12k+1=1+3+5+.......+2n-1.

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