Tamil Nadu Board of Secondary EducationHSC Arts Class 11th

# Find the sum up to the 17th term of the series 131+13+231+3+13+23+331+3+5+... - Mathematics

Sum

Find the sum up to the 17th term of the series 1^3/1 + (1^3 + 2^3)/(1 + 3) + (1^3 + 2^3 + 3^3)/(1 + 3 + 5) + ...

#### Solution

t1 = 1^3/1

t3 = (1^3 + 2^3)/(1 + 3)

t3 = (1^3 + 2^3 + 3^3)/(1 + 3 + 5)

∴ tn = (1^3 + 2^3 + 3^3 + ... :n:^3)/(1 + 3 + 5 + ... "n terms")

= (sum"n"^3)/("n"^2) ((2"n" - 1 + 1)/2)^2

= ("n"^2("n" + 1)^2)/(4("n"^2))

= ("n" + 1)^2/4

= ("n"^2 + 2"n" + 1)/4

∴ Sn = sum"t"_"n" = 1/4 sum"n"^2 + 2"n" + 1

= 1/4 sum"n"^2 + sum2"n" + sum1

= 1/4[("n"("n" + 1)(2"n" + 1))/6 + (2("n")("n" + 1))/2 + "n"]

To find S17 put n = 17

S17 = 1/4[(17 xx 18 xx 35)/6 + (2(17)(18))/2 + 17]

= 1/4[17 xx 105 + 17 xx 18 + 17]

= (17(105 + 18 + 1))/4

= 17 × 31

= 527

Concept: Finite Series
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#### APPEARS IN

Tamil Nadu Board Samacheer Kalvi Class 11th Mathematics Volume 1 and 2 Answers Guide
Chapter 5 Binomial Theorem, Sequences and Series
Exercise 5.3 | Q 2 | Page 220
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