Question

The n terms of the series 1+4/5+7/5²+10/5²+.... is
​

Answer 1

Answer:

Step-by-step explanation:

S∞ = 1 + 4/5 + 7/5² + 10/5³ + .............................

S∞/5 =    1/5 + 4/5² + 7/5³ + .......................

-              -    -        -

S∞(1-1/5) = 1 + 3/5 + 3/5² + 3/5³ + .............

4S∞/5 = 1 + 3/5(1 + 1/5 + 1/5² + .........................................)

4S∞/5 = 1 + 3/5(1/(1-1/5))

4S∞/5 = 1 + (3/5)(5/4)

4S∞/5 = 7/4

S∞ = 35/16

4Sn/5 = 1 + (3/5)[1{(1-1/5^n)/(1-1/5)}]

4Sn/5 = 1 + (3/5){5/4(1-1/5^n)]

4Sn/5 = 1 + (3/4)(1-1/5^n)

Sn = 5/4 + (15/16)(1-1/5^n)

or

Sn = 5/4 + (3/16)(5^n-1)/5^n-1

i hope you can understand .

Answer 2

Answer:

Step-by-step explanation:

The n terms of the series 1+4/5+7/5²+10/5²+.... is

​

S∞ = 1 + 4/5 + 7/5² + 10/5³ + .............................

S∞/5 =    1/5 + 4/5² + 7/5³ + .......................

-              -    -        -

S∞(1-1/5) = 1 + 3/5 + 3/5² + 3/5³ + .............

4S∞/5 = 1 + 3/5(1 + 1/5 + 1/5² + .........................................)

4S∞/5 = 1 + 3/5(1/(1-1/5))

4S∞/5 = 1 + (3/5)(5/4)

4S∞/5 = 7/4

S∞ = 35/16

4Sn/5 = 1 + (3/5)[1{(1-1/5^n)/(1-1/5)}]

4Sn/5 = 1 + (3/5){5/4(1-1/5^n)]

4Sn/5 = 1 + (3/4)(1-1/5^n)

Sn = 5/4 + (15/16)(1-1/5^n)

or

Sn = 5/4 + (3/16)(5^n-1)/5^n-1

i hope you can understand .