How did this conversion took place ?

[Sumedh]

Homework Statement

6(2)^(n-2) +1

then summation of above equation will be
6(2)^(n-1) + n + 2

can you please tell me how this equaton came from the first equation?

The Attempt at a Solution

the later formula is correct summation of the former

because it may look that the summation is
6(2)^(n-1) +n - 3

but by putting values of n-
6(2)^(n-1) +n - 3 is incorrect

please help as how the topmost formula gives the second formula

 

[Mark44]

Homework Statement

6(2)^(n-2) +1

then summation of above equation will be
6(2)^(n-1) + n + 2

can you please tell me how this equaton came from the first equation?

It doesn't. First off, these aren't equations - they are expressions. An equation is a statement that two expressions are equal, and always has an = symbol in it.

Starting from your first expression,
6$\cdot$2^n-2 + 1 = 6$\cdot$2^n-1$\cdot$(1/2) + 1 = 3$\cdot$2^n-1 + 1

To show that your two expressions above aren't identically equal, let n = 2. Then 6$\cdot$2^n-2 + 1 = 6 * 1 + 1 = 7.

And 6$\cdot$2^n-1 + n + 2 = 6* 2 + 2 + 2 = 16.

The Attempt at a Solution

the later formula is correct summation of the former

because it may look that the summation is
6(2)^(n-1) +n - 3

but by putting values of n-
6(2)^(n-1) +n - 3 is incorrect

please help as how the topmost formula gives the second formula

 

[eumyang]

I'm not sure what these expressions (and these are expressions, not equation) are. Are there any symbols missing? Can you attach an image, or retype using LaTeX?

 

[Sumedh]

the top most expressions are important and the last expression is what I am getting
this is one of the step of a problem in the book

http://books.google.co.in/books?id=Jp51spL2JOoC&pg=SA3-PA43&lpg=SA3-PA43&dq=find+the+general+term+and+sum+of+n+terms+of+the+series+9+16+29+54+103+iit&source=bl&ots=dqsJ7CsM7f&sig=kAbVnP2ZbXL7mycWs5OsGEPG3H4&hl=en&sa=X&ei=TawzT9LyHonorQfhg4SbDA&redir_esc=y#v=onepage&q&f=false

Page -3.43
topic -Sequence and series
example 7

 

[eumyang]

I get a "page is unavailable" error.

 

[Sumedh]

http://books.google.co.in/books?id=Jp51spL2JOoC&lpg=SA3-PA43&ots=dqsJ7CsM7f&dq=find%20the%20general%20term%20and%20sum%20of%20n%20terms%20of%20the%20series%209%2016%2029%2054%20103%20iit&pg=SA3-PA43#v=onepage&q&f=false