Question: b. Find a formula for the nth partial sum Sn of the infinite series. c. Make a conjecture for the value of the series. Select

b. Find a formula for the nth partial sum Sn of the infinite series.

c. Make a conjecture for the value of the series. Select the correct choice below?and, if?necessary, fill in the answer box to ~

Consider the following infinite series. Complete parts (a) through (c) below. k = 1 a. Find the first four partial sums S,, S2, S3, and S of the series. 21 85 SA 16 64 256 (Simplify your answers.) b. Find a formula for the nth partial sum S, of the infinite series. Sn = ,n21 Use the formula to find the next four partial sums Ss, S, S7, and S of the infinite series. 341 1365 5461 21845 S5 S.= 1024 4096 S7 16384 S8 65536 (Simplify your answers.) c. Make a conjecture for the value of the series. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The value of the infinite series is . (Type an integer or a simplified fraction.) O B. The infinite series has no value

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