1. Use Mathematical induction to prove the following: (a) 2n+1 ...

 

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1. Use Mathematical induction to prove the following: (a) 2n+1 <2", where n3. (b) 4"+5"+6" is divisible by 15 where n is an odd integer. 1 1 (c) + + - 1 + + 3.5 5.7 7.9 1 n = (2n+1) (2n+3) 3(2n+3 2. Find the sum of n terms of the series standard sums. n(n+1)(n+2) by using the three n=1 3. 53+x+y+25 form an arithmetic progression. Find x and y. 4. Find the two numbers whose arithmetic mean is 39 and geometric mean 15. 1. Use Mathematical induction to prove the following: (a) 2n+1 <2", where n3. (b) 4"+5"+6" is divisible by 15 where n is an odd integer. 1 1 (c) + + - 1 + + 3.5 5.7 7.9 1 n = (2n+1) (2n+3) 3(2n+3 2. Find the sum of n terms of the series standard sums. n(n+1)(n+2) by using the three n=1 3. 53+x+y+25 form an arithmetic progression. Find x and y. 4. Find the two numbers whose arithmetic mean is 39 and geometric mean 15.