The following series are neither arithmetic nor geometric, but by analyzing their patterns, you can find their sums. Find the sum of each series. ∑k=120(2k+k)

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The following series are neither arithmetic nor geometric, but by analyzing their patterns, you can find their sums. Find the sum of each series.  ∑k=120(2k+k)

amarantha41 · Accepted Answer

Step 1  We have to find the sum of the series  ∑k=120(2k+k)  Step 2  Now,  ∑k=120(2k+k)=∑k=1202k+∑k=120k  The series ∑k=1202k is a geometric series with first term  t1=21=2  common ratio r=2, and total number of terms n=20. Hence we have  ∑k=1202k=t1(rn−1)r−1=2(220−1)2−1=2(220−1)=2097150  The series ∑k=120k is an arithmetic series with first tem t1=1, last term t20=20, common difference d=1, and number of terms n=20  Hence we have  ∑k=120k=n(t1+tn)2=20(1+20)2=210  Thus  ∑k=120(2k+k)=∑k=1202k+∑k=120k=2097150+210=2097360

The following series are neither arithmetic nor geometric, but by

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