In the binomial expansion of (x ^ 2 + 1 / ax) ^ 6, the coefficient of x ^ 2 is 5 / 2, then a = need to answer the process in detail

In the binomial expansion of (x ^ 2 + 1 / ax) ^ 6, the coefficient of x ^ 2 is 5 / 2, then a = need to answer the process in detail

The quadratic term of (x ^ 2 + 1 / (AX)) ^ 6 is (x ^ 2) ^ n * x ^ - (6-n) 2n - (6-n) = 2n = 8 / 3, so there is no x ^ 2 term in this expansion
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Find (1 + x) ^ 3 + (1 + x) ^ 4 + +The coefficient of x ^ 3 in the expansion of (1 + x) ^ 20

C(3,3)+C(3,4)+C(3,5)+.C(3,20)
=C(4,4)+C(3,4)+C(3,5)+.C(3,20)
=C(4,5)+C(3,5)+.C(3,20)
=C(4,21)

Let the coefficient of X3 be - 581, then a = 0___ ，limn→∞(a+a2+… +an)= ___ ．

(1) From tr + 1 = c5r (AX) 5-r (- LX) r, it is concluded that when tr + 1 = (- 1) rc5ra5-rx5-2r, r = 1, that is (- 1) c51a4 = - 581, ｜ a = 13 +an=a×(1-an)1-a，∴limn→∞（a+a2+… +Method 2: from a = 13, we can know the sequence a, A2 If an is a decreasing equal ratio sequence, then LiMn →∞ (a + A2 +...) +An) denotes the sum of the items of the infinite decreasing equal ratio sequence. From the sum formula of the items of the infinite decreasing equal ratio sequence (LiMn →∞ Sn = a11-q), we can see LiMn →∞ (a + A2 +...) +So the answer is 12