Published by:
CGP EDU Academic Team
Published on: August 13, 2026
Find the sum of n terms of the series the r th term of which is (2r + 1)2 r .
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
n.2 n + 2 – 2 n + 1 + 2.
Sol. T r = (2r + 1) 2 r
S = 3.2 + 5.2 2 + 7.2 3 + .........+ (2n + 1) 2 n ...(i)
2S = 3.2 2 + 5.2 3 + .........+ (2n + 1) 2 n + (2n + 1) 2 n–1 ...(ii)
(i) – (ii) we get
– S = 3.2 + (2.2 2 + 2.2 3 + ......+ 2.2 n ) – (2n +1) 2 n+1 ⇒ – S = 6 + 8 (2 n–1 –1) – (2n + 1) 2 n+1
S = 2 – 2 n+2 + n. 2 n+2 + 2 n+1 ⇒ S = n.2 n+2 – 2 n+1 + 2
──────────────────────────────────────────────────────────────────────────────────────────
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems
Find the 4 th term of an H.P. whose 7 th term is and 13 th term is .
Insert three harmonic means between 1 and 7.
If = = and p, q, r are in A.P. then prove that x, y, z are in H.P.
If a 2 , b 2 , c 2 are in A.P. show that b + c , c + a, a + b are in H.P.
If b is the harmonic mean between a and c, then prove that + = .
Sum the following series
(i)1 + + + + ........ to n terms.
(ii) 1 + + + + + ..... to infinit…