214. 418. 8116. 16132................ is equal to
2
214. 418. 8116. 16132 .........∞
= 214+28+316+........ = 2S, where S is given by
S = 14 + 2 18 + 3 116 +4 132 + ............∞ .........(i)
⇒ 12 S = 18 + 216 + 332 + 464 + ................∞ ..........(ii)
Subtracting (ii) from (i), we get S = 1.
Hence required product = 21 = 2.