2. (10 points) (Exercise with summation) In this exercise you will prove that the pattern of numbers on the right below,

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2 10 Points Exercise With Summation In This Exercise You Will Prove That The Pattern Of Numbers On The Right Below 1 (49.23 KiB) Viewed 37 times

This path is more succint, but demands very preciselanguage.
(a) Find an explicit formula R(n) for the rightmost odd numberon the left hand side of the nth row above. For example, R(2)should yield 5, R(3) should be 11, and so on. Justify this formula- you must be able to prove this works always, not just for thefirst few.
(b) Now find a formula L(n) for the left most odd number in thenth row above. (So L(2) = 3, L(3) = 7). Justify this formula aswell.
(c) How many odd numbers are on the left hand side in the nthrow above?
(d) Using the previous three steps and the fact that each rowhas an even distribution to make an argument for what the value ofan should be. Thisneeds to be formally justified.
2. (10 points) (Exercise with summation) In this exercise you will prove that the pattern of numbers on the right below, an, is equal to n³. Two potential solutions have been outlined for you below. Pick one. 1 = a1 3+5 = a2 7+9+11 = a3 13 + 15 + 17 + 19 = as 21 +23+25+27 +29 = a5 ⠀⠀⠀