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Provide the first five terms of the sequence of partial sums for the given series.

n=1(1)nn2n!.

Short Answer

Expert verified

The first five terms of the partial sums for the seriesn=1(1)nn2n!is,-1,1,-12,-16,-924.

Step by step solution

01

Step 1. Given Information

n=1(1)nn2n!.

02

Step 2. Find the first term.

Substitute n=1in the given series.

(1)nn2n!=(1)1121!=-11=-1

The first term is,-1.

03

Step 3. Find the second term.

Substitute n=2in the given series.

(1)nn2n!=(1)2222!=142=2

The second term is,2.

04

Step 4. Find the third term.

Substitute n=3in the given series.

(1)nn2n!=(1)3323!=-196=-32

The third term is,-32

05

Step 5. Find the fourth term.

Substitute n=4in the given series.

(1)nn2n!=(1)4424!=1.1624=23

The fourth term is,23.

06

Step 6. Find the fifth term.

Substitute n=5in the given series.

(1)nn2n!=(1)5525!=-125120=-524

The fifth term is,-524.

07

Step 7. The first five terms in the sequence of the partial sums are,

S1=-1S2=S1+a2=-1+2=1S3=S2+a3=1-32=-12S4=S3+a4=-12+23=-16S5=S4+a5=-16-524=-924

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