Evaluate | Class 11 Mathematics Chapter Sequence and Series, Sequence and Series NCERT Solutions

Question:

Evaluate

$stack sum open parentheses 2 plus 3 to the power of k close parentheses with k equals 1 below and 11 on top$

Answer:

$stack sum space with k equals 1 below and 11 on top open parentheses 2 plus 3 to the power of k close parentheses equals sum from k equals 1 to 11 of open parentheses 2 close parentheses space plus space sum from k equals 1 to 11 of 3 to the power of k space equals space 2 open parentheses 11 close parentheses space plus space sum from k equals 1 to 11 of 3 to the power of k to the power of blank end exponent space equals 22 space plus space sum from k equals 1 to 11 of 3 to the power of k space space space space space space... open parentheses 1 close parentheses sum from k equals 1 to 11 of 3 to the power of k space equals space 3 to the power of 1 space plus space 3 squared space plus space 3 cubed space plus space... space plus space 3 to the power of 11 T h e space t e r m s space o f space t h i s space s e q u e n c e space 3 comma space 3 squared comma space 3 cubed comma space horizontal ellipsis space f o r m s space a space G. P. S subscript n space end subscript equals space fraction numerator a open parentheses r to the power of n space end exponent minus 1 close parentheses over denominator r minus 1 end fraction rightwards double arrow S subscript n space equals space fraction numerator 3 open square brackets open parentheses 3 close parentheses to the power of 11 space minus 1 close square brackets over denominator 3 minus 1 end fraction rightwards double arrow S subscript n space equals space 3 over 2 open parentheses 3 to the power of 11 space minus space 1 close parentheses therefore space space sum from k equals 1 to 11 of 3 to the power of k space equals space 3 over 2 open parentheses 3 to the power of 11 space minus 1 close parentheses S u b s t i t u t i n g space t h i s space v a l u e space i n space e q u a t i o n space left parenthesis 1 right parenthesis comma space w e space o b t a i n sum from k equals 1 to 11 of open parentheses 2 space plus space 3 to the power of k close parentheses space equals 22 space plus space 3 over 2 open parentheses 3 to the power of 11 space minus 1 close parentheses$

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Popular questions of class 11 Mathematics

Find the sum of integers from 1 to 100 that are divisible by 2 or 5.

If the sum of three numbers in A.P., is 24 and their product is 440, find the numbers.

A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second?

Q: Find the sum of all natural numbers lying between 100 and 1000, which are multiples of 5.

The sum of the first four terms of an A.P. is 56. The sum of the last four terms is 112. If its first term is 11, then find the number of terms.

How many terms of G.P. 3, 3², 3³, … are needed to give the sum 120?

Find the sum of all numbers between 200 and 400 which are divisible by 7.

Q: Write the following sets in roster form:
(i) A = {x: x is an integer and - 3 < x < 7}.
(ii) B = {x: x is a natural number less than 6}.
(iii) C = {x: x is a two-digit natural number such that the sum of its digits is 8}
(iv) D = {x: x is a prime number which is divisor of 60}.
(v) E = The set of all letters in the word TRIGONOMETRY.
(vi) F = The set of all letters in the word BETTER.

Insert five numbers between 8 and 26 such that the resulting sequence is an A.P.

Find the sum of all two digit numbers which when divided by 4, yields 1 as remainder.

Recently Viewed Questions of Class 11 Mathematics

If the sum of three numbers in A.P., is 24 and their product is 440, find the numbers.

One die of red colour, one of white colour and one of blue colour are placed in a bag. One die is selected at random and rolled, its colour and the number on its uppermost face is noted. Describe the sample space.

The 5th, 8th and 11th terms of a G.P. are p, q and s, respectively. Show that q² = ps.

Three coins are tossed once. Let A denote the event ‘three heads show”, B denote the event “two heads and one tail show”. C denote the event “three tails show” and D denote the event ‘a head shows on the first coin”. Which events are

(i) mutually exclusive? (ii) simple? (iii) compound?

Using Binomial Theorem, indicate which number is larger (1.1)¹⁰⁰⁰⁰ or 1000.

If the sum of first p terms of an A.P. is equal to the sum of the first q terms, then find the sum of the first (p + q) terms.

Find the equation of the circle with centre (0, 2) and radius 2

If a, b, c and d are in G.P. show that

$open parentheses a squared plus b squared plus c squared close parentheses open parentheses b squared plus c squared plus d squared close parentheses equals open parentheses a b plus b c plus c d close parentheses squared.$

Q: Find the sum of odd integers from 1 to 2001.

Solve 24x < 100, when
(i) x is a natural number. (ii) x is an integer.

Study Tips for Answering NCERT Questions:

NCERT questions are designed to test your understanding of the concepts and theories discussed in the chapter. Here are some tips to help you answer NCERT questions effectively:

Read the question carefully and focus on the core concept being asked.
Reference examples and data from the chapter when answering questions about Sequence and Series.
Review previous year question papers to get an idea of how such questions may be framed in exams.
Practice answering questions within the time limit to improve your speed and accuracy.
Discuss your answers with your teachers or peers to get feedback and improve your understanding.

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Welcome to the NCERT Solutions for Class 11 Mathematics - Chapter . This page offers a step-by-step solution to the specific question from Excercise 3 , Question 11: Evaluate ....

Evaluate | Class 11 Mathematics Chapter Sequence and Series, Sequence and Series NCERT Solutions

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