Question

Write the sum to n terms of a series whose rth term is r + $2^{r}$

Answer 1

Step-by-step explanation:

Given Write the sum to n terms of a series whose rth term is r + 2^r  

• We need to write the sum to n terms of a series whose r th term is r + 2^r
• Where r = 1,2,3……….n terms  
• So Sn = (1 + 2^1 + 2 + 2^2 + 3 + 2^3 + 4 + 2^4 + 5 + 2^5 +……….+ (n + 2^n)
• Or we can write this as
•  Sn = (1 + 2 + 3 + 4 + 5 +…….+ n)  + (2 + 2^2 + 2^3 + 2^4 + 2^5 +……..2^n )
•  Sn = n(n + 1) / 2 + 2 (2^n – 1 / 2 – 1)
•  Sn = n (n + 1) / 2 + 2 (2^n – 1 )
• Sn = n (n + 1) / 2 + (2 x 2^n – 2)
• Sn = n (n + 1) / 2 + 2^n + 1 - 2

Reference link will be

https://brainly.in/question/1261597