Math: Find the sum. Help?

Question

1) 1 + 3 +9 +....+2187

2) 1 - 1/2 + 1/ 4 - 1/8 +....- 1/512

Answer 1

1)

 The series is1 + 3 + 3² +...............3⁷

a = 1, r  =3 and ar^n-1 = 3⁷

33^n-1 = 3⁷

3ⁿ = 3⁷

n = 7

The sum of the series  = a(r) / r - 1 = 3(3^n-1) / 3 - 1

                                                                         = 3ⁿ / 2.

 

Answer 2

Geometric sum is

1) The geometric sum is 1 + 3 + 9 + .......+ 2187

Since

n th term is

Since bases are equal,equate the powers.

Therefore,

Answer 3

2) The geometric sum is

 

Since

Formula for sum of the sequence

Where a = first term, r = common ratio.

Formula for n th term

Since bases are equal,equate the powers.

Therefore,