Download App

Some Special Series — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsSome Special Series1 Mark
Question
Write the sum of the series $2 + 4 + 6 + 8 + ... + 2n$.
✓

Answer

Let $T_n$​​​​​​​ be the term of the given series and $S_n$​​​​​​​ be the sum of the given series.
$\therefore\ \text{T}_\text{n}=2\text{n}$
$\therefore\ \text{S}_\text{n}=\sum\limits^{\text{n}}_{\text{k}=1}\text{T}_\text{k}=\sum\limits^{\text{n}}_{\text{k}=1}2\text{k}$
$=2\sum\limits^{\text{n}}_{\text{k}=1}\text{k}$
$=2\Big[\frac{\text{n}(\text{n}+1)}{2}\Big]$
$=\text{n}(\text{n}+1)$
Hence, $\text{S}_\text{n}=\text{n}(\text{n}+1)$

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 "Solve the following Question.(1 Marks)" from Some Special Series→Some Special Series — all question types→Maths STD 11 Science question papers→Maharashtra Board STD 11 Science question papers→Maharashtra Board question paper generator→

Similar questions

The first and last terms of an A.P. are 1 and 11. If the sum of its terms is 36, then the number of terms will be:
  1. 5
  2. 6
  3. 7
  4. 8
→
Write down the following sets in set builder form:

{10, 20, 30, 40, 50}

→
Write the component statements of the following compound statements and check whether the compound statement is true or false:
Square of an integer is positive or negative.
→
Compute:

$\frac{6 !-4 !}{4 !}$

→
If the difference between the roots of the equation is $x^2 + ax + 8 = 0$ is $2$, write the values of a.
→
Find the middle term(s) in the expansion of $\left(x-\frac{1}{2 y}\right)^{10}$
→
Solve the following for $x$, where $|x|$ is modulus function, $[x]$ is the greatest integer function, $\{x\}$ is a fractional part function.

$\{x\}=0$

→
Write in terms of factorials $: 6 \times 7 \times 8 \times 9$
→
If the first term of the G.P. is 6 and its sum to infinity is $\frac{96}{17}$, find the common ratio.
→
Find the domain of

$f(x)=\log 10\left(x^2-5 x+6\right)$

→