1+13x+1×43×6x2+1×4×73×6×9x3+⋯ is equal to

Let,(1+y)n=1+13x+1×43×6x2+1×4×73×6×9x3+⋯ =1+ny+n(n−1)2!y2+⋯Comparing the terms, we getny=13x,n(n−1)2!y2=1×43×6x2Solving, n = -1/3, y = -x. Hence, the given series is (1 - x)-1/3.