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91Ó°ÊÓ

Evaluate the finite sums.

∑k=01000 2k.

Short Answer

Expert verified

The sum of the series∑k=01000 2kis,21001-1.

Step by step solution

01

Step 1. Given Information

∑k=01000 2k.

02

Step 2. Let us expand the given series.

∑k=01000 2k=1+2+4+...+21000

The first term in the series a=1.

The common ratior=2with the number of termsn=1001.

03

Step 3. The finite sum of the geometric series with ratio greater than 1 is given by,

Sn=arn-1r-1

Substitute the known values in the formula.

S1001=121001-12-1=21001-11=21001-1

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