k=0(1)k(k+14k+1)= ?

1 Answer
Mar 3, 2017

See below.

Explanation:

1(x+1)2=ddx(1x+1) but

1x+1=12+x1=12(11+x12)=12k=0(1)k(x12)k for x12<1

but

ddx(12k=0(1)k(x12)k)=122k=1(1)kk2k1(x1)k1=k=0(1)k(k+12k+2)(x1)k

Making x=12 we have

k=0(1)k(k+14k+1)=1(12+1)2=(23)2