Question: using induction prove this a b c d using induction prove this a b c d using induction prove this a b c d Using

using induction prove this a b c d using induction prove this a b c d using induction prove this a b c d

Using induction or a direct proof, prove the following identities (a) 1 + 8 + $2 + - - - + all1 = 11:3: for real number :5 51$ 1 and any natural number n. (b) a" b\" = (a b)(a\"_1 + (In2b + - - - + Min2 + (In1) for any real numbers a and b and any natural number n. (c) 1 :5 +592 + - - - m2k_1 + mm\" = \"13:\" for any real number a: # 1 and any natural number k. (d) a2k+1 +132\"lrl = (a+b)(a2k :.r,2\"\"_ll)+ugh2b2 - - -ab2k_1 +b2k) for any real numbers a and b and any natural number k

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