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Question

Find the 20th term and the sum of 20 terms of the series :

2×4+4×6+6×8+....


Solution

Here the nth term of the series is Tn=2n(2n+2) Thus the 20th term will be T20=2×20(2×20+2)=1680 The infinite series can be written as : 2×4+4×6+6×8+...=20n12n(2n+1) Therefore the sum up to 20th term will be =20n12n(2n+1)=20n14n2+20n14n=420n1n2+420n1n=4.20(20+1)(2.20+1)6+4.20(20+1)2 =12320


Mathematics
RD Sharma
Standard XI

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