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# 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}) = 3^{1} + 3^{2} + 3^{3} + .... + 3^{11}

The terms of this sequence 3, 3^{2}, 3^{3} .... forms a G.P

Therefore,

S_{n} = 3 (3^{11} - 1)/(3 - 1)

= 3/2 (3^{11} - 1)

Substituting this value in (1) , we obtain

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

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