Sequences and Series 5 Question 23

14. Let Sk, where k=1,2,,,100, denotes the sum of the infinite geometric series whose first term is k1k! and the common ratio is 1k. Then, the value of 1002100!+k=1100|(k23k+1)Sk| is …..

(2010)

Assertion and Reason

For the following question, choose the correct answer from the codes (a), (b), (c) and (d) defined as follows:

(a) Statement I is true, Statement II is also true; Statement II is the correct explanation of Statement I

(b) Statement I is true, Statement II is also true; Statement II is not the correct explanation of Statement I

(c) Statement I is true; Statement II is false

(d) Statement I is false; Statement II is true

Show Answer

Solution:

  1. Given, a1a2a3an=c

a1a2a3(an1)(2an)=2c

a1+a2+a3++2ann(a1a2a32an)1/n

[using AMGM ]

a1+a2+a3++2ann(2c)1/n

[from Eq. (i)]

Minimum value of

a1+a2+a3++2an=n(2c)1/n



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