Question

Problem 3. Write the summation with the first two terms and the last term outside of the summation. Use the sequences from 1(a) and 1(d) to complete this problem. 10 j-2 m-+2 3(b) Let m 20. dk

Answer 1

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Below is the answer

a)

Since ai is GP with a=8 and r=2

So, the nth term of sequuence is a*r^n-1

So, the summation with first and last 2 outside are

So, summation=

=

b)

Since kth term is first k+1 positive odds

So, d0=1

d1=1+3=4

d_(m+1)=1+3+5+.... (m+2 terms)

((m+2)/2)*(2+2(m+1))=(m+2)^2

d_(m+2)=1+3+5+....(m+2 terms)

((m+3)/2)*(2+2*(m+2))=(m+3)^2

So, the summation is

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