Title: Arithmetic and Geometric Series Title: Mathematical Induction Part 1 1. For everyr natural number n prove the proposition P(") given by 1+2+3+4+...+n =ln(n+1) n 2. For every natural number prove the proposition P(") given by 1+3+5+7+...+ 2n1 =n2 n 3. Prove that for every natural number the proposition P(") given by n(n+l)(2n+1) 12 +22 +32 +...+ri2 = Title: Arithmetic and Geometric Series |. Arithmetic Series 1. Evaluate the related series of the sequence. 6, 11, 16, 21. 26, 31, 36. 2. Evaluate the arithmetic series described by 3. Find20+27+34+41 +...,n= 16 4. Given , , , nd the value of n. II. Geometric Series 1. Evaluate the related series of the sequence, 2, 12, 72, 432. 2. Evaluate the geometric series described by . 3. Find the value of 1 4 + 16-64 n = 9. 4. Given , , , find the value of n