Question
Question: Sum of the series 1 + 2.2 + 3.2<sup>2</sup> + 4.2<sup>3</sup>+ ....+100.2<sup>99</sup> is –...
Sum of the series 1 + 2.2 + 3.22 + 4.23+ ....+100.299 is –
A
(100)2100 + 1
B
(99)2100 + 1
C
(99) 299 –1
D
100(2100)–1
Answer
(99)2100 + 1
Explanation
Solution
S = 1 + 2.2 + 3.22 + ....100.299
2S = 2 + 2.22 + .........+100.210
– S = (1 + 2 + 22 .........100 term) – 100.2100
– S = 1.(2100 – 1) – 100.2100
S = 100.2100 –2100 + 1 = 99.2100 + 1