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The value of 4+2 (1+2)log 2 +(2(1+2^(2)...

The value of `4+2 (1+2)log 2 +(2(1+2^(2))/(2!) (log2)^(2) +(2(1+2^(3))/(3!) (log2)^(3) +…` is

A

10

B

12

C

`log(3^(2).4^(2))`

D

`log(2^(2).3^(2))`

Text Solution

Verified by Experts

The correct Answer is:
b
` 4+2 (1+2) log 2 +(2(1+2)^(2)(log2)^(2))/(2!)`
` + (2(1+2)^(3)(log2)^(3))/(3!)+...`
` = 2(1+log2 + ((log2)^(3))/(2!) +... )`
` +2(1+2log 2+((2log2)^(2))/(2!)+...)`
` 2(e^(log 2)) +2(e^(2log 2)) = 2xx 2+2e^(log4)`
` = 4 +2 xx 4 = 12`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-SEQUENCES AND SERIES -EXERCISE 26
  1. The value of 4+2 (1+2)log 2 +(2(1+2^(2))/(2!) (log2)^(2) +(2(1+2^(3))...

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