33 C
Maharashtra
Friday, June 9, 2023
HomeGeneral AptitudeWhat will be the sum of n terms of the series whose...

What will be the sum of n terms of the series whose ​\( n^{th} \)​ term is ​\( 5.3^{n+1}+2n \)​?

- Advertisement -

Question:

What will be the sum of n terms of the series whose ​\( n^{th} \)​ term is ​\( 5.3^{n+1}+2n \)​?

Answer:

Here ​\( a_n=5.3^{n+1}+2n \)​ 
We have have to find ​\( s_n \)​.
\( \therefore s_n=\displaystyle\sum_{k=1}^{n}a_k \)​ 
\( \therefore s_n=\displaystyle\sum_{k=1}^{n}\left(5.3^{k+1}+2k\right) \)
\( \therefore s_n=\displaystyle\sum_{k=1}^{n}5.3.3^k+\displaystyle\sum_{k=1}^{n}2k \)
\( \therefore s_n=15\displaystyle\sum_{k=1}^{n}3^k+2\displaystyle\sum_{k=1}^{n}k \)​ 
\( \therefore s_n=15[3\left(\frac{3^n-1}{3-1}\right)]+2[\frac{n(n+1)}{2}] \)
\( \therefore s_n=\frac{45}{2}(3^n-1)+n(n+1) \)
- Advertisement -
RELATED ARTICLES

LEAVE A REPLY

Please enter your comment!
Please enter your name here

- Advertisment -

Most Popular

Insert math as
Block
Inline
Additional settings
Formula color
Text color
#333333
Type math using LaTeX
Preview
\({}\)
Nothing to preview
Insert