Evaluate ∑¹¹_{k = 1}(2 + 3^k)

Solution:

∑¹¹_{k = 1}(2 + 3^k) = ¹¹∑_{k = 1}(2) + ¹¹∑_{k = 1}(3^k)

= 22 + ¹¹∑_{k = 1}(3^k) ....(1)

Now,

¹¹∑_{k = 1}(3^k) = 3¹ + 3² + 3³ + .... + 3¹¹

The terms of this sequence 3, 3², 3³ .... forms a G.P

Therefore,

S_n = 3 (3¹¹ - 1)/(3 - 1)

= 3/2 (3¹¹ - 1)

Substituting this value in (1) , we obtain

∑¹¹_{k = 1}(2 + 3^k) = 22 + 3/2 (3¹¹ - 1)

NCERT Solutions Class 11 Maths Chapter 9 Exercise 9.3 Question 11

Evaluate ∑¹¹_{k = 1}(2 + 3^k)

Summary:

To evaluate ∑¹¹_{k = 1}(2 + 3^k) we had to individually calculate the terms and then get the answer which is 22 + 3/2 (3¹¹ - 1)