Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11

# Write the Sum to N Terms of a Series Whose Rth Term is R + 2r. - Mathematics

Short Note

Write the sum to n terms of a series whose rth term is r + 2r.

#### Solution

Series whose rth term is r + 2r

$\left( 1 + 2^1 \right) + \left( 2 + 2^2 \right) + \left( 3 + 2^3 \right) + \left( 4 + 2^4 \right) + . . . + \left( n + 2^n \right)$

Thus, we have:

$S_n = \left( 1 + 2^1 \right) + \left( 2 + 2^2 \right) + \left( 3 + 2^3 \right) + \left( 4 + 2^4 \right) + . . . + \left( n + 2^n \right)$
$= \left( 1 + 2 + 3 + 4 + . . . + n \right) + \left( 2 + 2^2 + 2^3 + 2^4 + . . . + 2^n \right)$
$= \frac{n\left( n + 1 \right)}{2} + 2\left( \frac{2^n - 1}{2 - 1} \right)$
$= \frac{n\left( n + 1 \right)}{2} + 2^{n + 1} - 2$

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 21 Some special series
Q 3 | Page 19