1.2 + 2.2 ² + 3.2 ² + … + n .2 ⁿ = ( n – 1) 2 ^{n +1} + 2

this question is solved on this site...... but I can't understand how the final answer came ..... please see 4.1's 8th question on this site ......

from equatoin 1

(k-1)2^k+1+2+k+1.2^k+1=k2^k+2+2

l.h.s,

2^{k+1_(k-1+k+1)+2}

=2^k+1(2.k)+2

=k2^k+1+1+2

=k2^k+2+2

didn't understand ........ in NCERT solution , how the final answer came ? please explain that .........

P(1):1*2¹=2=(1-1)2^1-1+2

.^..P(1) is True