problem 4 consider the following sequence en and of partial sums sz where sn eez en for example

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Problem 4. Consider the following sequence En and the partial sums Sz, where Sn = E1 + Ez + ... + En For example, since we know E1 = 1 and Ez = âˆš4, we calculate S2 = E1 + Ez = 1 + (-4) = -3 Register Entry (En) Sum (Sn) 1 1 2 -3 3 ? 4 ? Fill in the missing items in this table; where question marks appear: This means finding entries and the row of partial sums S3, S4, etc. Based on your findings, find a closed form algebraic expression in terms of n that will give you Sn. Prove (by induction) that the pattern you found in part (a) holds. Make sure you have the correct closed form pattern from part (a) to do this. If unsure, check with me. Show that the formula you found for Sn holds when n is the base (that is, when Sn = 1). Complete the inductive step: show that if Sn holds, then the formula Sn+1 equals the formula you found in part (a), that En = (-1)^n in terms of n + 1. (You may use the fact n^2 = n squared without proof). CSULB

          Problem 4. Consider the following sequence En and the partial sums Sz, where
Sn = E1 + Ez + ... + En

For example, since we know E1 = 1 and Ez = âˆš4, we calculate S2 = E1 + Ez = 1 + (-4) = -3

Register Entry (En)  Sum (Sn)
1                  1
2                  -3
3                  ?
4                  ?

Fill in the missing items in this table; where question marks appear: This means finding entries and the row of partial sums S3, S4, etc. Based on your findings, find a closed form algebraic expression in terms of n that will give you Sn. Prove (by induction) that the pattern you found in part (a) holds. Make sure you have the correct closed form pattern from part (a) to do this. If unsure, check with me.

Show that the formula you found for Sn holds when n is the base (that is, when Sn = 1). Complete the inductive step: show that if Sn holds, then the formula Sn+1 equals the formula you found in part (a), that En = (-1)^n in terms of n + 1. (You may use the fact n^2 = n squared without proof).

CSULB

problem 4 consider the following sequence en and of partial sums sz where sn eez en for example since we know e 1and ez 4 we calculate s2 eez 1 4 8 register entry en sum sn 233 fill in the m 53783

Added by Garrett C.

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