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Evaluate the finite sums.

k=010012k

Short Answer

Expert verified

The sum of the seriesk=010012kis,2-12100.

Step by step solution

01

Step 1. Given Information

k=010012k.

02

Step 2. Let us expand the given series.

k=010012k=1+12+122+....+12100.

The first term in the series, a=1.

The common ratio is, r=12with number of termsn=101.

03

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

Sn=a1-rn1-r

Substitute the known values in the formula.

S101=11-121011-12=1-1210112=21-12101=2-12100

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