1. Use sigma notation to rewrite the following infinite series. Starting with n = 1. (a)...

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1. Use sigma notation to rewrite the following infinite series. Starting with n = 1. (a) 1- 1 1 +- 1 +... 2 3 4 (b) 11+11+1 1+ 1 2 3 4 ++ + 2 4 8 16 +.... 2. Compute the first 4 partial sums S1, S2, S3, S4 for the following series: n n=1 3. State whether the given geometric series converges or diverges and explain why. If it is convergent, please find its sum S. 1 10 100 1000 1 (a) 1+ + 1 + +... e2 e3 73 e (b) 1+ + (c) n=1 3 () 2 n=1 n n 4 (=)" + +. 1. Use sigma notation to rewrite the following infinite series. Starting with n = 1. (a) 1- 1 1 +- 1 +... 2 3 4 (b) 11+11+1 1+ 1 2 3 4 ++ + 2 4 8 16 +.... 2. Compute the first 4 partial sums S1, S2, S3, S4 for the following series: n n=1 3. State whether the given geometric series converges or diverges and explain why. If it is convergent, please find its sum S. 1 10 100 1000 1 (a) 1+ + 1 + +... e2 e3 73 e (b) 1+ + (c) n=1 3 () 2 n=1 n n 4 (=)" + +.