Evaluate the following: _ n=1 ^ 11 (2+3^n) - Vidyadip

Question

Evaluate the following:$\sum_\limits{\text{n}=1}^{11}(2+3^\text{n})$

✓

Answer

$\sum_\limits{\text{n}=1}^{11}(2+3^\text{n})$ $=(2+3^1)+(2+3^2)+(2+3^3)+\ \dots\ +(2+3^{11})$ $=2\times11+3^1+3^2+3^3+\dots+3^{11}$ $=22+\frac{3(3^{11}-1)}{(3-1)}$ $=22+\frac{3(3^{11}-1)}{2}$ $=\frac{44+3(177147-1)}{2}$ $=\frac{44+3(177146)}{2}$ $=265741$ So, $\sum_\limits{\text{n}=1}^{11}(2+3^\text{n})=265741$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "(Each question 3 marks)" from Geometric Progressions→Geometric Progressions — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Show the following quadratic equation: $ix^2 - x + 12i = 0$

$\text{a}^2\sin(\text{B}-\text{C})=(\text{b}^2-\text{c}^2)\sin\text{A}$

A rod of length $12 m$ moves with its ends always touching the coordinates axes. Determine the equation of the locus of a point P on the rod, which is $3 cm$ from the end in contact with the X-axis.

Differentiate the following function with respect to x:$(\text{x}\sin\text{x}+\cos\text{x})(\text{e}^\text{x}+\text{x}^2\log\text{x})$

Evaluate the following limit: $\lim\limits_{\text{x}\rightarrow{\infty}}\frac{5\text{x}^3-6}{\sqrt{9+4\text{x}^6}}$

The sum of 4th and 8th terms of an A.P. is 24 and the sum of the 6th and 10th terms is 34. Find the first term and the common difference of the A.P.

Show that the path of a moving point such that its distances from two lines 3x – 2y = 5 and 3x + 2y = 5 are equal is a straight line.

Evaluate the following limit: $\lim\limits_{\text{x}\rightarrow{\infty}}{\sqrt{\text{x}+1}-\sqrt{\text{x}}}{}$

Solve the following equations: $\tan3\text{x}+\tan\text{x}=2\tan2\text{x}$

How many words, with or without meaning, each of 2 vowels and 3 consonants can be formed from the letters of the word DAUGHTER.