Prove Propositions 32 and 33 of the Maasei Hoshev: a) 1 + (1 + 2) + (1 + 2 + 3) + ... + (1 + 2 + ... + n) =    1 2 + 32 + ... + n 2 , if n is odd; 2 2 + 42 + ... + n 2 , if n is even.

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the law of definite proportions states samples of a compound will always contain the same proportion of elements by mass. in other words, a given compound will always contain the same elements in the same proportions by mass.the law of multiple proportions states when two elements combine with each other to form more than one compound, then the weights of one element that combine with a fixed weight of the other are in a ratio of small whole numbers.