Find the first six partial sums S1, S2, S3, S4, S5, S6 of the sequence whose nth term is given.

Question

1
2
,
1
22
,
1
23
,
1
24
, . . .
S1
=
S2
=
S3
=
S4
=
S5
=
S6
=

Answer 1

S1 = 1
S2 = 1 + 2 = 3
S3 = 1 + 2 + 1/22 = 3 + 1/22 = 3.0454 (rounded to four decimal places)
S4 = 1 + 2 + 1/22 + 1/23 = 3 + 1/22 + 1/23 = 3.0904 (rounded to four decimal places)
S5 = 1 + 2 + 1/22 + 1/23 + 1/24 = 3 + 1/22 + 1/23 + 1/24 = 3.1333 (rounded to four decimal places)
S6 = 1 + 2 + 1/22 + 1/23 + 1/24 + 1/25 = 3 + 1/22 + 1/23 + 1/24 + 1/25 = 3.1730 (rounded to four decimal places)