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Let T(n) = 1 + 2 + ... + n be the n-th triangular number. For...

Let T(n) = 1 + 2 + ... + n be the n-th triangular number. For example, t(1) = 1, t(2) = 3, t(3) = 6... T(n)= n(n+1)/ 2

a. Show that T(2n) = 3T(n) + T(n-1)

b. Show that T(1) + T(2) + T(n) = (n(n+1)(n+2))/6

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