Question

Find the sum of the terms of a GP 1 + 2/3 + 3/32 + 4/33 + 5/34 + ……​

Answer 1

Answer:

From the question, it is given that,

Sum of the terms S

n

=3069/512

First term a=3

Common ratio r=(3/2)/3

=(3/2)×(1/3)

=1/2

We know that,

S

n

=a(1−r

n

)/(1−r)

(3069/512)=3[1−(1/2)

n

]/(1−1/2)

(3069/512)=(2×3)[1−(1/2)

n

]

1−(1/2)

n

=3069/(512×6)

1−(1/2)

n

=1023/1024

(1/2)

n

=1−(1023/1024)

(1/2)

n

=(1024−1023)/1024

(1/2)

n

=1/1024

(1/2)

n

=(1/2)

10

By comparing both LHS and RHS, n=10

Therefore, there are 10 terms are in the G.P.

Answer 2

Answer:

6/35+7/36+8/37+9/38+10/39